<PAGE>

                                                                 Exhibit 10.1
                                                                 ------------

                                FIRST AMENDMENT
                                       TO
              AMENDED AND RESTATED SECURITIES PURCHASE AGREEMENT,
                              STANDSTILL AGREEMENT
                                      AND
                         REGISTRATION RIGHTS AGREEMENT

     This First Amendment to Amended and Restated Securities Purchase Agreement,
Standstill Agreement and Registration Rights Agreement (this "Amendment") is
entered into as of July 12, 2001 by and between Cabletron Systems, Inc., a
Delaware corporation (the "Company"), Silver Lake Partners, L.P., a Delaware
limited partnership ("Silver Lake"), and the other Investors listed on the
signature page hereto.

     WHEREAS, the Company and Silver Lake are parties to an Amended and Restated
Securities Purchase Agreement, dated as of August 29, 2000 (the "Securities
Purchase Agreement"), a Standstill Agreement, dated as of August 29, 2000 (the
"Standstill Agreement"), and a Registration Rights Agreement, dated as of August
29, 2000 (the "Registration Rights Agreement");

     WHEREAS, the Company, Silver Lake and the other Investors desire to amend
certain terms of the Securities Purchase Agreement, the Standstill Agreement and
the Registration Rights Agreement as set forth herein;

     NOW, THEREFORE, in consideration of the mutual promises hereinafter set
forth, the parties hereto hereby agree as follows:

1.  Definitions.  Capitalized terms used and not otherwise defined herein shall
    -----------
have the meanings set forth in the Securities Purchase Agreement.

2.  Amendment to Securities Purchase Agreement.
    ------------------------------------------

     2.1.  Amendment to Section 1.5(c) of Securities Purchase Agreement.
           ------------------------------------------------------------
Section 1.5(c) of the Securities Purchase Agreement is hereby amended and
restated in its entirety to read as follows:

     "(c)  The Replacement Warrants (i) will be immediately exercisable upon
     issuance (provided that they shall in any event become exercisable no later
     than immediately prior to the consummation of the triggering third-party
     acquisition, in the case of an event described in Section 1.5(a)(iii)
     above), and will remain exercisable until the later of (a) the fourth
     anniversary of the Closing or (b) the first anniversary of the consummation
     of the Purchase Right Flip-Up Event giving rise to the issuance of such
     Replacement Warrants, (ii) will have an initial aggregate exercise price
     equal to the product of (A) 5 2/3, multiplied by (B) the exercise price in
     effect for the related Callable Subsidiary Stock Purchase Rights
     immediately prior to such Purchase Right Flip-Up Event (subject to the
     following


<PAGE>

     proviso), (iii) will initially be exercisable for that percentage of the
     Company's diluted Common Stock equal to the product of (A) that percentage
     of the diluted common stock of the Operating Subsidiary for which the
     related Subsidiary Stock Purchase Rights were (or when issued, would have
     been) exercisable immediately prior to the consummation of such Purchase
     Right Flip-Up Event multiplied by (B) a fraction the numerator of which is
     the Flip-Up Valuation and the denominator of which is the market
     capitalization of the Company immediately preceding such Purchase Right
     Flip-Up Event, and (iv) otherwise will be on the terms and conditions set
     forth in the form of Parent Warrant; provided, however, that, in the case
                                          --------  -------
     of a Purchase Right Flip-Up Event described in clause (i) or clause (ii) of
     the definition thereof occurring prior to the second anniversary of the
     Closing, the initial aggregate exercise price of the Replacement Warrants
     shall be discounted, and shall equal the product of (A) 5 2/3, multiplied
     by (B) the exercise price in effect for the related Callable Subsidiary
     Stock Purchase Rights immediately prior to such Purchase Right Flip-Up
     Event, multiplied by (C) 0.9."

     2.2. Issuance of Subsidiary Warrants in Connection with Spin-Off. The
          -----------------------------------------------------------
Section acknowledge and agree that the Company intends to consummate a Spin-Off
of Riverstone (the "Riverstone Spin"). For the avoidance of doubt, the parties
further agree that the calculations set forth in the attached Exhibit A reflect
                                                              ---------
the proper application of Section 1.7 of the Securities Purchase Agreement in
connection with the Riverstone Spin, and, based on the assumptions set forth in
Exhibit A, (a) the exercise price per share of Common Stock under the Class A
---------
Parent Warrants and the Class B Parent Warrants outstanding on the date of the
Riverstone Spin would be adjusted as set forth in the attached Exhibit A, and
                                                               ---------
(b) the Company would cause Riverstone to issue to the Investors Subsidiary
Warrants with respect to the Class A Parent Warrants and Class B Parent Warrants
exercisable for the number of shares of common stock of Riverstone, and the
exercise price per share, set forth in the attached Exhibit A.  Subject to the
                                                    ---------
foregoing, such Subsidiary Warrants shall have such other terms as are described
in the Securities Purchase Agreement.

     2.3. Issuance of Replacement Warrants in Connection with Purchase Right
          ------------------------------------------------------------------
Flip-Up Event. The parties acknowledge and agree that the Company intends to
-------------
consummate a merger of Enterasys with and into the Company (the "Enterasys Flip-
Up Event") and that, in the event that the Riverstone Spin occurs within one
hundred and twenty days of the date hereof, the Riverstone Spin shall be deemed
to have occurred prior to the consummation of the Enterasys Flip-Up Event for
all purposes of the Securities Purchase Agreement and the issuance of
Replacement Warrants in connection with the Enterasys Flip-Up Event. The parties
further agree that, in the event that the Enterasys Flip-Up Event is consummated
within ninety days of the date hereof, pursuant to Section 1.5 of the Securities
Purchase Agreement (and notwithstanding anything in Section 1.5(c)(ii) or
1.5(c)(iii) to the contrary) in connection with the Enterasys Flip-Up Event, (a)
the Subsidiary Stock Purchase Rights issued to the Investors by Enterasys shall
be canceled, and (b) the Company shall issue to the Investors Replacement
Warrants exercisable for an aggregate of 7,400,000 shares of Common Stock, with
an aggregate exercise price of $45,880,000. Subject to the foregoing, such
Replacement Warrants shall have such other terms as are described in the
Securities Purchase Agreement.

                                      -2-
<PAGE>

     2.4. Further Notifications. The Company shall have no further obligation to
          ---------------------
provide the Investors with notice of the Riverstone Spin or the Enterasys Flip-
Up Event, provided that the Company consummates each of the foregoing upon the
          --------
terms and within the time periods contemplated by this Amendment and its
Exhibits.

     2.5.  References to the Company's Series A and Series B Participating
           ---------------------------------------------------------------
Convertible Preferred Stock.  Upon the consummation of the exchange by the
---------------------------
Company pursuant to a Securities Exchange Agreement among the parties hereto,
dated as of July 12, 2001, of the Company's Series D and Series E Participating
Convertible Preferred Stock for the outstanding shares of the Company's Series A
and Series B Participating Convertible Preferred Stock issued pursuant to the
Securities Purchase Agreement (the "Exchange"), (a) the references in Sections
5.5, 5.6, 6.1 and 9.4 of the Securities Purchase Agreement to the "Shares" shall
be deemed to be references to the Company's Series D and Series E Participating
Convertible Preferred Stock, and (b) the references in Section 5.7 of the
Securities Purchase Agreement to the "Shares" issued by the Company to the
Investors on the Closing Date shall be deemed to be references to the Company's
Series D and Series E Participating Convertible Preferred Stock, which shall be
deemed to have been outstanding as of the Closing Date for purposes of Section
5.7 of the Securities Purchase Agreement.

3.  Amendment to Standstill Agreement.  Upon the consummation of the Exchange,
    ---------------------------------
Section 1.01(p) of the Standstill Agreement is hereby amended and restated in
its entirety to read as follows:

          "(p)        "Preferred Stock" shall mean the Company's Series D and
     Series E Participating Convertible Preferred Stock, $1.00 par value per
     share."

4.  Amendment to Registration Rights Agreement.  Upon the consummation of the
    ------------------------------------------
Exchange, references in the Registration Rights Agreement to the "Preferred
Stock" shall be deemed to be references to the Company's Series D and Series E
Participating Convertible Preferred Stock and shall be deemed to include any
preferred stock or other securities issued upon a recapitalization of the
Company's Series D and Series E Participating Convertible Preferred Stock,
except where the context requires otherwise.

5.  Miscellaneous.
    -------------

    5.1. Full Force and Effect. Except to the extent specifically amended
          ---------------------
hereby, the provisions of the Securities Purchase Agreement and the Standstill
Agreement shall remain unmodified, and each of the Securities Purchase Agreement
and the Standstill Agreement shall continue in full force and effect.

    5.2. Governing Law. This Amendment shall be governed in all respects by the
         -------------
laws of the State of Delaware, exclusive of its conflict-of-law principles.  The
Company hereby submits to the non-exclusive jurisdiction of the courts of the
State of New York, and the Investors hereby submit to the non-exclusive
jurisdiction of the courts of the State of New Hampshire, in each case for the
purpose of any suit, proceeding or judgment with respect to this Amendment.
Each of the parties hereto hereby irrevocably and unconditionally waives trial
by jury in any legal action or proceeding in relation to this Amendment and for
any counterclaim therein.

                                      -3-
<PAGE>

     5.3. Severability. In case any provision of this Amendment shall be
          ------------
invalid, illegal or unenforceable, the validity, legality and enforceability of
the remaining provisions shall not in any way be affected or impaired thereby.

     5.4. Amendment and Waiver. This Amendment may be amended or modified, and
          --------------------
the rights of the Company or the Investors hereunder may only be waived, upon
the written consent of the Company and the Majority Investors.

     5.5. Titles and Subtitles. The titles of the sections and subsections of
          --------------------
this Amendment are for convenience of reference only and are not to be
considered in construing this Amendment.

     5.6. Counterparts; Execution by Facsimile Signature. This Amendment may be
          ----------------------------------------------
executed in any number of counterparts, each of which shall be an original, but
all of which together shall constitute one instrument.  This Amendment may be
executed by facsimile signature(s).

                                      -4-
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have executed this First Amendment
to Amended and Restated Securities Purchase Agreement, Standstill Agreement and
Registration Rights Agreement as of the date set forth in the first paragraph
hereof.

The Company:          CABLETRON SYSTEMS, INC.


                      By /s/ Piyush Patel
                        -------------------------------
                        Name: Piyush Patel
                        Title: President and CEO


The Investors:        SILVER LAKE PARTNERS, L.P.

                      By: Silver Lake Technology Associates, L.L.C.,
                          its general partner


                      By: /s/ Jim Davidson
                         ------------------------------
                        Name: Jim Davidson
                        Title: Managing Member


                      SILVER LAKE INVESTORS, L.P.

                      By: Silver Lake Technology Associates, L.L.C.,
                          its general partner


                      By: /s/ Jim Davidson
                         ------------------------------
                        Name: Jim Davidson
                        Title: Managing Member


                      SILVER LAKE TECHNOLOGY
                      INVESTORS, L.L.C.

                      By: Silver Lake Technology Associates, L.L.C.,
                          its managing member


                      By: /s/ Jim Davidson
                         ------------------------------
                        Name: Jim Davidson
                        Title: Managing Member
<PAGE>

                      MORGAN STANLEY DEAN WITTER EQUITY
                      FUNDING, INC.


                      By: /s/ James T. Keane
                         ------------------------------
                        Name:  James T. Keane
                        Title: Vice President

                      INTEGRAL CAPITAL PARTNERS V, L.P.

                      By: Integral Capital Management V, LLC,
                          its general partner


                      By: /s/ Pamela Hagenah
                         ------------------------------
                        Name: Pamela Hagenah
                        Title: Manager

                      INTEGRAL CAPITAL PARTNERS V
                      SIDE FUND, L.P.

                      By: ICP Management V, LLC,
                          its general partner


                      By: /s/ Pamela Hagenah
                         ------------------------------
                        Name: Pamela Hagenah
                        Title: Manager

                      ORIGINATORS INVESTMENT PLAN, L.P.

                      By: MSDW OIP Investors, Inc.,
                          its general partner


                      By: /s/ James T. Keane
                         ------------------------------
                        Name: James T. Keane
                        Title:  Vice President

                                      -6-
<PAGE>

                                   Exhibit A
                              to First Amendment
                                      to
              Amended and Restated Securities Purchase Agreement
                           and Standstill Agreement

Cabletron Systems Inc
Subsidiary Warrants
Estimated as of July 27 Record Date & August 6 Distribution Date (TM)


<TABLE>
<S>                                                            <C>               <C>               <C>              <C>
RSTN Subsidiary Warrants (on CS's Investor Warrants)

Facts Assumed (to be adjusted based on actuals):
RSTN common shares prior to additional contribution                                92,088,235
Additional RSTN shares in pre-spin-off contribution                                 8,000,000
                                                                                 ------------
Total RSTN shares to be distributed by CS                                         100,088,235
                                                                                 ============

Cabletron o/s Shares at RSTN Spin record date                                     188,315,621
CS Preferred D&E Stock on an as converted basis                                     2,549,842
CS Investor Warrants                                                                  450,000
                                                                                 ------------
CS shares or equivalent shares at record date                                     192,315,445
                                                                                 ============
CS per share price at close on 8/7/2001 (post-spin)**               $10.00
RSTN per share price at close on 8/7/2001 (post-spin)**             $20.00
                                                                                                                    Total Subsidiary
                                                                                 $35 Warrants     $45 Warrants           Warrants
Investor Parent Warrants                                           (A)                200,000          250,000
                                                                                 ------------     ------------

RSTN Share held by Cabletron                                       (B)            100,088,235      100,088,235
                                                                                 ------------     ------------

CSI O/S Stock @ 5/16/2001                                                         188,815,621      188,815,621
Additional CS shares - 5/16/2001 - Record Date                                        500,000          500,000
Investor Preferred Stock @ 7/27/2001                                                2,549,824        2,549,824
Investor Parent Warrants                                                              450,000          450,000
                                                                                 ------------     ------------
                                                                   (C)            192,315,445      192,315,445
                                                                                 ============     ============

RSTN Subsidiary Warrants                                       (A)X(B)+(C)            104,088          130,109             234,197
                                                                                 ============     ============        ============

RSTN Subsidiary Warrants                                            (D)               104,088          130,109
RSTN per share price at open on 8/7/2001(post-spin)                 (E)               $ 20.00          $ 20.00
                                                                                 ------------     ------------
          RSTN Warrant Market Value (D)X(E)                         (F)             2,081,751        2,602,189
                                                                                 ============     ============

CS Parent Warrants                                                  (G)               200,000          250,000
CS per share price at open on 8/7/2001(post-spin)                   (H)               $ 10.00          $ 10.00
                                                                                 ------------     ------------
          CS Warrant Market Value (G)X(H)                           (I)             2,000,000        2,500,000
                                                                                 ============     ============

          Initial Warrant Price                                     (K)               $ 35.00          $ 45.00
          RSTN Allocation (F)+[(F)+(I)]                             (L)                 51.00%           51.00%
                                                                                 ------------     ------------
          RSTN per share warrant price (L)X(M)                                        $17,850          $22,951
                                                                                 ============     ============

          Initial Warrant Price                                     (M)               $ 35.00          $ 45.00
          CS Allocation (I)+[(F)+(I)]                               (N)                 49.00%           49.00%
                                                                                 ------------     ------------
          CS per share warrant price (M)X(N)                                          $17,150          $22,049
          Initial Warrant Price                                     (O)                35,000           45,000
                                                                                 ------------     ------------
          Strike Price Reduction (N)-(O)                                             ($17,850)        ($22,951)
                                                                                 ============     ============
</TABLE>

*  Actual record date and distribution date will be used to make final
   caculations.

** Final calculations will be based on the applicable shre price as of the first
   trading day following the acrual distribution date.