<PAGE>   1

                                                                 Exhibit 10.7.1




                 FIRST AMENDMENT TO THREE-YEAR CREDIT AGREEMENT

         This FIRST AMENDMENT TO THREE-YEAR CREDIT AGREEMENT (this
"Amendment"), dated as of June 20, 2000, is by and among LINCARE HOLDINGS INC.,
a Delaware corporation (the "Borrower"), each of the Borrower's Subsidiaries
(individually a "Guarantor" and collectively the "Guarantors"; together with
the Borrower, individually a "Credit Party", and collectively the "Credit
Parties"), the Required Lenders signatory hereto and BANK OF AMERICA, N. A., as
Agent for the Lenders (in such capacity, the "Agent").

         W I T N E S S E T H

         WHEREAS, the Credit Parties, the Lenders and the Agent have entered
into that certain Three-Year Credit Agreement dated as of August 23, 1999 (the
"Existing Credit Agreement");

         WHEREAS, the Borrower has requested, and the Lenders have agreed, to
amend certain provisions of the Existing Credit Agreement as more fully set
forth below.

         NOW, THEREFORE, in consideration of the agreements hereinafter set
forth, and for other good and valuable consideration, the receipt and adequacy
of which are hereby acknowledged, the parties hereto agree as follows:


                                     PART I
                                  DEFINITIONS

         SUBPART 1.1       Certain Definitions. Unless otherwise defined herein
or the context otherwise requires, the following terms used in this Amendment,
including its preamble and recitals, have the following meanings:

                  "Amended Credit Agreement" means the Existing Credit
         Agreement as amended hereby.

                  "Amendment No. 1 Effective Date" is defined in Subpart 4.1.

         SUBPART 1.2       Other Definitions. Unless otherwise defined herein
or the context otherwise requires, terms used in this Amendment, including its
preamble and recitals, have the meanings provided in the Existing Credit
Agreement.

<PAGE>   2

                                    PART II
                    AMENDMENTS TO EXISTING CREDIT AGREEMENT

         Effective on (and subject to the occurrence of) the Amendment No. 1
Effective Date, the Existing Credit Agreement is hereby amended in accordance
with this Part 2.

         SUBPART 2.1       Amendments to Section 1.1. Section 1.1 of the
Existing Credit Agreement is hereby amended in the following respects:

                  (a)      The definition of "Change of Control" is hereby
         amended in its entirety to read as follows:

                           "Change of Control" means the occurrence of any of
                  the following events: (i) any Person or two or more Persons
                  acting in concert (other than Persons owning 30% or more of
                  the Voting Stock of the Borrower on the Closing Date) shall
                  have acquired beneficial ownership, directly or indirectly,
                  of, or shall have acquired by contract or otherwise, or shall
                  have entered into a contract or arrangement that, upon
                  consummation, will result in its or their acquisition of,
                  control over, Voting Stock of the Borrower (or other
                  securities convertible into such Voting Stock) representing
                  30% or more of the combined voting power of all Voting Stock
                  of the Borrower, (ii) any Person or two or more Persons
                  acting in concert (other than Persons owning 30% or more of
                  the Voting Stock of the Borrower on the Closing Date) has the
                  ability directly or indirectly, to elect a majority of the
                  board of directors of the Borrower, (iii) during any period
                  of up to 12 consecutive months, commencing on the Closing
                  Date, individuals who at the beginning of such 12-month
                  period were directors of the Borrower shall cease for any
                  reason (other than the death, disability or retirement of an
                  officer of the Borrower that is serving as a director at such
                  time so long as another officer of the Borrower replaces such
                  Person as a director) to constitute a majority of the board
                  of directors of the Borrower; provided, however to the extent
                  there exist vacancies on the Board of Directors as of the
                  Closing Date or if after the Closing Date, the existing Board
                  of Directors increases the number of directors on the Board
                  of Directors by an amount not more than three, the
                  individuals named to fill such vacancies, if selected by a
                  majority of directors sitting as of the Closing Date, shall
                  be deemed for purposes of this clause (iii) to have been
                  appointed prior to the Closing Date or (iv) the occurrence of
                  a "Change of Control" under the Senior Note Purchase
                  Agreements, the Senior Notes, or other documents evidencing
                  the Senior Notes.

                  (b)      The definition of "Permitted Acquisition" is hereby
         amended in its entirety to read as follows:

                           "Permitted Acquisition" means an Acquisition by the
                  Borrower or any Subsidiary of the Borrower for the fair
                  market value of the Capital Stock or Property acquired,
                  provided that (i) the Capital Stock or Property acquired in
                  such



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                  Acquisition relates to a line of business similar to the
                  business of the Borrower or any of its Subsidiaries, (ii) in
                  the case of an Acquisition of Capital Stock of another
                  Person, (A) the board of directors (or other comparable
                  governing body) of such other Person shall have duly approved
                  such Acquisition and (B) such Person shall become a
                  wholly-owned direct or indirect Subsidiary of the Borrower,
                  (iii) the representations and warranties made by the Credit
                  Parties in any Credit Document shall be true and correct in
                  all material respects at and as if made as of the date of
                  such Acquisition (after giving effect thereto) except to the
                  extent such representations and warranties expressly relate
                  to an earlier date and no Default or Event of Default exists
                  as of the date of such Acquisition (after giving effect
                  thereto) and (iv)(A) if the aggregate consideration for such
                  Acquisition, exceeds $25,000,000 but is less than
                  $35,000,000, the Borrower shall have delivered to the Agent a
                  Pro Forma Compliance Certificate demonstrating that, upon
                  giving effect to the Acquisition on a Pro Forma Basis, the
                  Borrower will be in compliance with all of the financial
                  covenants set forth in Section 7.11 or (B) if the aggregate
                  consideration (including cash and non-cash consideration and
                  any assumption of Indebtedness) for such Acquisition exceeds
                  $35,000,000 or if any such Acquisition would cause the
                  aggregate consideration for all Acquisitions in any fiscal
                  year to exceed $150,000,000, the Borrower shall have received
                  the approval of the Required Lenders, which approval shall be
                  given in the Required Lenders' sole discretion; provided,
                  however, that with respect to clause (B) above for fiscal
                  year 2000 only, if the aggregate consideration (including
                  cash and non-cash consideration and any assumption of
                  Indebtedness) for any Acquisition consummated after the
                  consummation of the United Medical Acquisition exceeds
                  $35,000,000 or if any such additional Acquisition would cause
                  the aggregate consideration for all Acquisitions consummated
                  after the consummation of the United Medical Acquisition to
                  exceed $50,000,000, the Borrower shall have received the
                  approval of the Required Lenders.

                  (c)      The definition of "Pledge Agreement" is hereby
         amended in its entirety to read as follows:

                           "Pledge Agreement" means (i) prior to the first date
                  on which the Borrower has issued any Senior Notes, the pledge
                  agreement dated as of the Closing Date in the form of Exhibit
                  1.1(a), as amended, modified, restated or supplemented from
                  time to time and (ii) thereafter, the "New Pledge Agreement"
                  described in Subpart 3.2(b) of Amendment No. 1, as amended,
                  modified, restated or supplemented from time to time.

                  (d)      The following new definitions are added to
         Section 1.1 of the Existing Credit Agreement in appropriate
         alphabetical order:

                           "Amendment No. 1" means that certain First Amendment
                  to Three-Year Credit Agreement dated as of June 20, 2000 by
                  and among the Borrower, the Guarantors, the Required Lenders
                  signatory hereto and the Agent.



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<PAGE>   4



                           "Intercreditor Agreement" means an intercreditor
                  agreement dated as of a date on or before July 31, 2000 and
                  in form and substance reasonably satisfactory to the Agent,
                  defining the relationship between the Agent and the Lenders,
                  on the one hand, and the Noteholders, on the other hand, with
                  respect to the relative rights and priorities with respect to
                  the Pledged Collateral and providing for the sharing of any
                  amounts recovered pursuant to the obligations of the
                  Guarantors under Section 4 and the guaranties of the Senior
                  Notes permitted under Section 8.1(j).

                           "Senior Note Purchase Agreements" means a collective
                  reference to note purchase agreements, dated as of a date on
                  or before July 31, 2000 and in form and substance reasonably
                  satisfactory to the Agent, among the Borrower and each of the
                  Senior Noteholders.

                           "Senior Noteholders" means a collective reference to
                  the holders from time to time of the Senior Notes and "Senior
                  Noteholder" means any one of them.

                           "Senior Notes" means a collective reference to
                  senior notes in an aggregate principal amount of up to
                  $150,000,000, and in form and substance reasonably
                  satisfactory to the Agent, to be issued by the Borrower on or
                  before July 31, 2000 pursuant to the Senior Note Purchase
                  Agreements, as such Senior Notes may be amended, modified,
                  restated or supplemented and in effect from time to time in
                  accordance with the terms thereof. The Senior Notes shall
                  rank pari passu with the Credit Party Obligations in priority
                  of payment and shall be secured by a lien on the Pledged
                  Collateral ranking pari passu with the lien of the Agent
                  therein.

                           "United Medical Acquisition" means the Acquisition
                  by the Borrower, on or prior to June 30, 2000, of
                  substantially all of the assets of United Medical, Inc., an
                  Arkansas corporation, for aggregate consideration of
                  approximately $123,000,000.

         SUBPART 2.2       Amendments to Section 8.1. Clauses (h) and (i) of
Section 8.1 of the Existing Credit Agreement are hereby amended in their
entireties to read as follows and the following new clauses (j) and (k) are
added to such Section immediately thereafter:

                  8.1      INDEBTEDNESS.

                  The Credit Parties will not permit any Consolidated Party to
         contract, create, incur, assume or permit to exist any Indebtedness,
         except:

                                ****************

                           (h)      Indebtedness owing by one Credit Party to
                  another Credit Party;



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                           (i)      other Indebtedness hereafter incurred by
                  the Borrower not exceeding $10,000,000 in aggregate principal
                  amount at any time outstanding;

                           (j)      Indebtedness of the Borrower arising under
                  the Senior Note Purchase Agreements and the Senior Notes in
                  an aggregate principal amount of up to $150,000,000; provided
                  that (i) the final maturity date of such Senior Notes occurs
                  after the Maturity Date and (ii) such Senior Note Purchase
                  Agreements and Senior Notes do not contain terms and
                  conditions which, when taken as a whole, are more restrictive
                  that the terms and conditions of the Credit Agreement; and

                           (k)      Guaranty Obligations of any Guarantor with
                  respect to the Indebtedness of the Borrower permitted under
                  Section 8.1(j).

         SUBPART 2.3       Amendments to Section 8.11. Section 8.11 of the
Existing Credit Agreement is hereby amended in its entirety to read as follows:

                  8.11     LIMITATION ON RESTRICTED ACTIONS.

                  The Credit Parties will not permit any Consolidated Party to,
         directly or indirectly, create or otherwise cause or suffer to exist
         or become effective any encumbrance or restriction on the ability of
         any such Person to (a) pay dividends or make any other distributions
         to any Credit Party on its Capital Stock or with respect to any other
         interest or participation in, or measured by, its profits, (b) pay any
         Indebtedness or other obligation owed to any Credit Party, (c) make
         loans or advances to any Credit Party, (d) sell, lease or transfer any
         of its properties or assets to any Credit Party, (e) grant a lien on
         its properties or assets whether now owned or hereafter acquired or
         (f) act as a Guarantor and pledge its assets pursuant to the Credit
         Documents or any renewals, refinancings, exchanges, refundings or
         extension thereof, except (in respect of any of the matters referred
         to in clauses (a)-(d) above) for such encumbrances or restrictions
         existing under or by reason of (i) this Credit Agreement and the other
         Credit Documents, (ii) the Senior Note Purchase Agreements and the
         Senior Notes or (iii) applicable law.

         SUBPART 2.4       Amendments to Section 8.14. Section 8.14 of the
Existing Credit Agreement is hereby amended in its entirety to read as follows:

                  8.14     NO FURTHER NEGATIVE PLEDGES.

                  Except (a) pursuant to this Credit Agreement and the other
         Credit Documents, (b) pursuant to the Senior Note Purchase Agreements
         and the Senior Notes and (c) pursuant to any document or instrument
         governing Indebtedness incurred pursuant to Section 8.1(c), provided
         that any such restriction contained therein relates only to the asset
         or assets constructed or acquired in connection therewith, the Credit
         Parties will not permit any Consolidated Party to enter into, assume
         or become subject to any agreement prohibiting or otherwise
         restricting the creation or assumption of any Lien upon its properties
         or assets, whether now owned or hereafter acquired, or requiring the
         grant of any security for such obligation if security is given for
         some other obligation.



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<PAGE>   6

                                    PART III
                          CONSENT, AUTHORIZATION, ETC.

         SUBPART 3.1       United Medical Acquisition. The Required Lenders
hereby consent to the United Medical Acquisition.

         SUBPART 3.2       Execution of Intercreditor Agreement and Restated
Pledge Agreement; Indemnification of Collateral Agent.

                  (a)      The Required Lenders hereby authorize and direct the
         Agent, on behalf of the Lenders, at such time as any Senior Notes
         shall be issued by the Borrower, to execute and deliver (i) the
         Intercreditor Agreement and (ii) a pledge agreement (the "New Pledge
         Agreement") amending and restating the Pledge Agreement for the
         purpose of providing that the Pledged Collateral shall be held by Bank
         of America as a collateral agent for the ratable benefit of the
         Lenders and the Senior Noteholders (in such capacity, the "Collateral
         Agent").

                  (b)      The Credit Parties agree that, at such time as the
         Intercreditor Agreement and the New Pledge Agreement shall have become
         effective:

                           (i)      to pay to the Collateral Agent all of its
                  out-of-pocket expenses in connection with the preparation,
                  execution and delivery of the Intercreditor Agreement and the
                  New Pledge Agreement and the transactions contemplated
                  thereby, including but not limited to the reasonable charges
                  and disbursements of counsel;

                           (ii)     to pay to the Collateral Agent from time to
                  time reasonable compensation for all services rendered by it
                  under the Intercreditor Agreement and the New Pledge
                  Agreement;

                           (iii)    to reimburse the Collateral Agent upon its
                  request for all reasonable expenses, disbursements and
                  advances incurred or made by the Collateral Agent in
                  accordance with any provision of the Intercreditor Agreement
                  or the New Pledge Agreement (including the reasonable
                  compensation and the expenses and disbursements of its agents
                  and counsel); and

                           (iv)     to indemnify the Collateral Agent for, and
                  to hold it harmless against, any loss, liability or expense
                  incurred without gross negligence or willful misconduct on
                  the part of the Collateral Agent, arising out of or in
                  connection with the Intercreditor Agreement or the New Pledge
                  Agreement or any action taken or omitted by it thereunder or
                  in connection therewith, including, but not limited to, the
                  costs and expenses of defending itself against any claim or
                  liability in connection with the exercise or performance of
                  any of its powers or duties hereunder, and any loss,
                  liability, expense or claim arising out of its possession,
                  management, control, use or operation of the Pledged
                  Collateral.



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<PAGE>   7

                  (c)      At such time as the Intercreditor Agreement and the
         New Pledge Agreement shall have become effective, the Lenders shall be
         required to indemnify the Collateral Agent (to the extent not
         reimbursed by the Credit Parties), ratably with the Senior
         Noteholders, for any and all liabilities, obligations, losses,
         damages, penalties, actions, judgments, suits, costs, expenses or
         disbursements of any kind and nature whatsoever that may be imposed
         on, incurred by or asserted against the Collateral Agent, without
         gross negligence or willful misconduct on the part of the Collateral
         Agent, arising out of the actions of the Collateral Agent under the
         Intercreditor Agreement or the New Pledge Agreement or the
         transactions contemplated thereby or the enforcement of any of the
         terms thereof. The Lenders shall be subrogated to the rights of the
         Collateral Agent with respect to all amounts paid by it pursuant to
         this clause (b), and all such amounts shall constitute Credit Party
         Obligations.


                                    PART IV
                          CONDITIONS TO EFFECTIVENESS

         SUBPART 4.1       Amendment No. 1 Effective Date. This Amendment shall
be and become effective as of June 20, 2000 (the "Amendment No. 1 Effective
Date") when all of the conditions set forth in this Part 4 shall have been
satisfied, and thereafter this Amendment shall be known, and may be referred
to, as "Amendment No. 1."

         SUBPART 4.2       Execution of Counterparts of Amendment. The Agent
shall have received counterparts of this Amendment, which collectively shall
have been duly executed on behalf of each of the Borrower, the Guarantors and
the Lenders.

         SUBPART 4.3       Other Items. The Agent shall have received such
other documents, agreements or information which may be reasonably requested by
the Agent.


                                     PART V
                                 MISCELLANEOUS

         SUBPART 5.1       Representations and Warranties. The Borrower hereby
represents and warrants to the Agent and the Lenders that, after giving effect
to this Amendment, (a) no Default or Event of Default exists under the Credit
Agreement or any of the other Credit Documents and (b) the representations and
warranties set forth in Section 6 of the Existing Credit Agreement are, subject
to the limitations set forth therein, true and correct in all material respects
as of the date hereof (except for those which expressly relate to an earlier
date).

         SUBPART 5.2       Reaffirmation of Credit Party Obligations. Each
Credit Party hereby ratifies the Credit Agreement and acknowledges and
reaffirms (a) that it is bound by all terms of the Credit Agreement applicable
to it and (b) that it is responsible for the observance and full performance of
its respective Credit Party Obligations.



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<PAGE>   8

         SUBPART 5.3       Cross-References. References in this Amendment to
any Part or Subpart are, unless otherwise specified, to such Part or Subpart of
this Amendment.

         SUBPART 5.4       Instrument Pursuant to Existing Credit Agreement.
This Amendment is a Credit Document executed pursuant to the Existing Credit
Agreement and shall (unless otherwise expressly indicated therein) be
construed, administered and applied in accordance with the terms and provisions
of the Existing Credit Agreement.

         SUBPART 5.5       References in Other Credit Documents. At such time
as this Amendment No. 1 shall become effective pursuant to the terms of Subpart
4.1, all references in the Credit Documents to the "Credit Agreement" shall be
deemed to refer to the Credit Agreement as amended by this Amendment No. 1.

         SUBPART 5.6       Counterparts/Telecopy. This Amendment may be
executed by the parties hereto in several counterparts, each of which shall be
deemed to be an original and all of which shall constitute together but one and
the same agreement. Delivery of executed counterparts of the Amendment by
telecopy shall be effective as an original and shall constitute a
representation that an original shall be delivered.

         SUBPART 5.7       Governing Law. THIS AMENDMENT SHALL BE DEEMED TO BE
A CONTRACT MADE UNDER AND GOVERNED BY THE INTERNAL LAWS OF THE STATE OF
NEW YORK.

         SUBPART 5.8       Successors and Assigns. This Amendment shall be
binding upon and inure to the benefit of the parties hereto and their
respective successors and assigns.

         SUBPART 5.9       General. Except as amended hereby, the Existing
Credit Agreement and all other Credit Documents shall continue in full force
and effect.



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<PAGE>   9

         IN WITNESS WHEREOF, each of the parties hereto has caused a
counterpart of this Amendment to be duly executed and delivered as of the date
first above written.

BORROWER:                           LINCARE HOLDINGS INC.,
                                    a Delaware corporation


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


GUARANTORS:                         LINCARE INC.,
                                    a Delaware corporation


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    LINCARE PROCUREMENT INC.,
                                    a Delaware corporation


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    LINCARE ASSET MANAGEMENT LP,
                                    a Nevada limited partnership
                                             BY: LINCARE HOLDINGS INC., A
                                             DELAWARE CORPORATION, ITS GENERAL
                                             PARTNER


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    LINCARE OF NEW YORK INC.,
                                    a New York corporation


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------



<PAGE>   10



                                    LINCARE PHARMACY SERVICES INC.,
                                    a Delaware corporation


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    LINCARE LICENSING INC.,
                                    a Delaware corporation


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    CONVACARE SERVICES INC.,
                                    an Indiana corporation


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    LINCARE TRAVEL INC.,
                                    a Delaware corporation


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------



<PAGE>   11

LENDERS:                            BANK OF AMERICA, N. A.,
                                    individually in its capacity as a
                                    Lender and in its capacity as Agent


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    BANKATLANTIC


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    BANK LEUMI LE - ISRAEL B.M.,
                                    MIAMI AGENCY


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    COMERICA BANK


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    BANKERS TRUST COMPANY


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    FLEET NATIONAL BANK


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


<PAGE>   12

                                    THE FUJI BANK, LIMITED


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    THE INDUSTRIAL BANK OF JAPAN
                                    LIMITED


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    MICHIGAN NATIONAL BANK


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    SCOTIABANC INC.


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    CREDIT LYONNAIS NEW YORK BRANCH


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------


                                    U.S. BANK NATIONAL ASSOCIATION


                                    By:
                                          -------------------------------------
                                    Name:
                                          -------------------------------------
                                    Title:
                                          -------------------------------------