<PAGE>

                                                                    Exhibit 10.8

                          SECOND SUPPLEMENTAL AGREEMENT

            SECOND SUPPLEMENTAL AGREEMENT, dated the 15th day of December, 1999
and effective with respect to the payment of rent and other charges with respect
to the Remaining 9th Floor Portion (as that term is hereinafter defined) as more
particularly set forth in Article 3 below as of the 1st day of December, 1999,
by and among 345 PARK AVENUE SOUTH PARTNERS LLC, a New York limited liability
company having an office c/o RFR Holding LLC, 400 Park Avenue, New York, New
York 10022 (hereinafter called "Landlord"), THE NEW YORK LAW PUBLISHING COMPANY,
a New York corporation having an office at 345 Park Avenue South, New York, New
York (hereinafter called "Tenant") and AMERICAN LAWYER MEDIA, INC. a Delaware
corporation having an office at 345 Park Avenue South, New York, New York
(hereinafter called "ALM").

                            W I T N E S S E T H :

            WHEREAS:

            A. Landlord's predecessor-in-interest, Park Avenue South/Armory,
Inc. ("Landlord's Predecessor-in Interest"), and Tenant have heretofore entered
into a certain lease, dated as of September 30, 1993 (the "Original Lease"),
which Original Lease was amended by that certain First Supplemental Agreement
(the "First Supplemental Agreement"), dated as of November 30, 1994. The
Original Lease, as amended by the First Supplemental Agreement as aforesaid, and
as the same may have been heretofore further amended, is hereinafter
collectively called the "Lease"). Pursuant to the Original Lease, Landlord's
Predecessor-in-Interest leased to Tenant, and Tenant leased from Landlord's
Predecessor-in-Interest, the entire seventh (7th) and eighth (8th) floors, and a
certain portion of the ninth (9th) floor as more particularly described in the
Original Lease (hereinafter sometimes referred to as the "Original 9th Floor
Portion"), and a portion of the basement floor (hereinafter collectively called
the "Original Demised Premises") in the building (hereinafter called the
"Building") known as 345 Park Avenue South, New York, New York for a term ending
on August 31, 2008 (which date is defined in the Original Lease as the
"Expiration Date"), upon which said term may expire or be terminated pursuant to
any conditions of limitation or other provisions of the Lease or pursuant to
law.

            B. Pursuant to the First Supplemental Agreement, Landlord's
Predecessor-in-Interest leased to Tenant, and Tenant leased from Landlord's
Predecessor-in-Interest, an additional portion of the ninth (9th) floor as more
particularly described in the First Supplemental Agreement (hereinafter referred
to as the "Added 9th Floor Portion"). Hereinafter the Original 9th Floor Portion
and the Added 9th Floor are collectively referred to as the "Leased 9th Floor
Portions", and that portion of the ninth (9th) floor of the Building which is
not part of the Leased 9th Floor Portions is hereinafter referred to as the
"Remaining 9th Floor Portion." Landlord and Tenant now desire to add the
Remaining 9th Floor Portion to the premises demised under the Lease and to
otherwise modify the Lease as hereinafter provided.

            C. Effective as of the date hereof, Tenant desires to assign all of
Tenant's right, title and interest in and to the Lease (as amended by this
Second Supplemental Agreement) to ALM, and Landlord is willing to permit Tenant
to assign the Lease (as amended by this
<PAGE>

Second Supplemental Agreement), subject to and in accordance with the terms and
conditions hereinafter set forth.

            NOW, THEREFORE, in consideration of the premises and mutual
covenants hereinafter contained, the parties hereto hereby modify the Lease as
follows:

            1. All capitalized terms contained in this Second Supplemental
Agreement which are not defined herein shall, for the purposes hereof, have the
meanings as are ascribed to them in the Lease.

            2. Effective as of the date hereof (the "Adjustment Date") and
continuing for the period commencing on the Adjustment Date and ending on the
Expiration Date (hereinafter called the "Adjustment Period"), there shall be
added to, and included in, the premises demised under the Lease, the Remaining
9th Floor Portion as shown approximately hatched on the plan annexed hereto and
made a part hereof as Exhibit A.

            In order to accomplish such addition and inclusion of the Remaining
9th Floor Portion to and in the premises demised under the Lease, Landlord does
hereby lease to Tenant, and Tenant does hereby hire from Landlord, the Remaining
9th Floor Portion upon and subject to all the covenants, agreements, terms, and
conditions of the Lease as supplemented by this Second Supplemental Agreement
continuing for the period commencing on the Adjustment Date through and
including the Adjustment Period.

            Landlord and Tenant acknowledge and agree that the inclusion of the
Remaining 9th Floor Portion into the premises demised under the Lease as
provided in this Second Supplemental Agreement is being granted by Landlord and
accepted by Tenant in lieu of the provisions of Article 46 of the Original Lease
and that said Article 46 is hereby deemed null and void and of no force or
effect.

            3. The following terms and conditions shall be effective during the
Adjustment Period with regard to the Remaining 9th Floor Portion only:

                  (a) The fixed annual rent payable pursuant to Article 1 of the
Lease shall be increased as follows:

                        (i) for the period beginning on December 1, 1999 through
                  and including May 31, 2004 by the sum of $394,272.00 per
                  annum; and

                        (ii) for the period beginning on June 1, 2004 through
                  the Expiration Date, by the sum of $427,128.00 per annum.

                  (b) With respect to the adjustments of rent set forth in
Article 3 of the Lease (hereinafter called the "Initial Adjustments") there
shall be computed, in addition to the Initial Adjustments, adjustments of rent
with respect to increases of Taxes and Operating Expenses attributable to the
Remaining 9th Floor Portion. Adjustments of rent with respect to Taxes and
Operating Expenses with respect to the Remaining 9th Floor Portion will be
computed in the same manner as adjustments of rent with respect to Taxes and
Operating Expenses for the purpose of the Initial Adjustments, except that, for
the purpose of such computation with respect


                                       2
<PAGE>

to the Remaining 9th Floor Portion, the following adjustments shall apply (which
adjustments shall be in addition to Tenant's continuing obligation to pay the
Initial Adjustments with respect to increases in Taxes and Operating Expenses in
respect of the premises heretofore demised under the Lease):

                        (i) The Base Tax, as defined in Section 3.01(a) of the
                  Lease shall mean fifty (50%) percent of the Taxes for the Tax
                  Years commencing July 1, 1999 and July 1, 2000 as finally
                  determined.

                        (ii) The Base Operating Expense Amount, as defined in
                  Section 3.01 (f) of the Lease, shall be the Operating Expenses
                  for the calendar year 2000.

                        (iii) Tenant's Proportionate Tax Share, as defined in
                  Section 3.01(b) of the Lease, shall be deemed to mean 4.24
                  (4.24%) percent, calculated as the fraction, expressed as a
                  percentage, the numerator of which shall be 10,952 which
                  Landlord and Tenant agree for purposes of the Lease
                  constitutes the rentable square footage of the Remaining 9th
                  Floor Portion, and the denominator of which is 258,438, which
                  Landlord and Tenant agree constitutes the rentable square
                  footage of the Building for Purposes of calculating Tenant's
                  Proportionate Tax Share.

                        (iv) Tenant's Proportionate Operating Share, as defined
                  in Section 3.01(h) of the Lease, shall be deemed to mean 4.51
                  (4.51%) percent, calculated as the fraction, expressed as a
                  percentage, the numerator of which is 10,952, which Landlord
                  and Tenant agree for purposes of the Lease constitutes the
                  rentable square footage of the Remaining 9th Floor Portion,
                  and the denominator of which is 242,638, which Landlord and
                  Tenant agree constitutes the rentable square footage of the
                  office space in the Building for purposes of calculating
                  Tenant's Proportionate Operating Share.

                        (v) The term "Operating Year", as defined in Section
                  3.01(e) of the Lease, shall mean the calendar year 2000 and
                  each succeeding year occurring during the term of the Lease.

                        (vi) The term "Base Year", as defined in Section 3.01(e)
                  of the Lease, shall mean the calendar year 2000.

                        (vii) Notwithstanding anything set forth in the Lease or
                  in this Agreement to the contrary, Tenant's obligation to pay
                  escalations in respect of increases of Taxes and Operating
                  Expenses in respect of the Remaining 9th Floor Portion only
                  shall commence on January 1, 2001.

                  (c) Tenant acknowledges that the electricity for the Remaining
9th Floor Portion shall be provided by means of a separate electric sub-meter
servicing the Remaining 9th Floor Portion in accordance with Article 4 of the
Lease, except, with respect to the


                                       3
<PAGE>

Remaining 9th Floor Portion only, all references in Article 4 of the Lease to
103% shall be deemed changed to 104.5%.

            4. Tenant shall use the Remaining 9th Floor Portion for the purposes
set forth in the Lease, and for no other purpose. Tenant acknowledges that it is
fully familiar with all aspects of the conditions within the Remaining 9th Floor
Portion and that Landlord has made no representation to Tenant with respect to
the physical condition of the Remaining 9th Floor Portion and Tenant agrees to
accept the Remaining 9th Floor Portion "AS IS" as of the Adjustment Date
(subject to latent defects and any pre-existing hazardous materials) and further
agrees that no materials are to be furnished by Landlord and no work whatever is
to be performed by Landlord in connection with the premises heretofore demised
under the Lease or the Remaining 9th Floor Portion or any part of either,
except, that on the Adjustment Date, the Remaining 9th Floor Portion shall be
delivered with the Building's heating, ventilation, air-conditioning,
electrical, plumbing and sprinkler systems servicing the Remaining 9th Floor
Portion in good working order and on the Adjustment Date the Remaining 9th Floor
Portion shall be delivered "broom clean" and free of all tenancies.
Notwithstanding anything set forth herein or in the Lease to the contrary,
Tenant shall not be required to cure any violations with respect to the
Remaining 9th Floor Portion only which were noted or issued of record prior to
the date hereof. Landlord shall deliver the Remaining 9th Floor Portion in the
condition required herein on the date Tenant executes, acknowledges and delivers
to Landlord an original of this Agreement.

            5. Effective as of the date hereof, provided ALM is and remains an
Affiliate of Tenant, Landlord hereby consents to an assignment by Tenant of all
of Tenant's right, title and interest in and to the Lease to ALM (an
"Assignment"), provided that:

                  (a) The Landlord's consent as hereinabove set forth shall not
be construed in any manner to modify, waive or affect any of the terms,
covenants, conditions or agreements contained in the Lease, or to waive any
breach or default by Tenant under the Lease.

                  (b) Tenant shall not be released from, and Tenant shall be and
remain liable for, the performance and observance of all of the terms,
covenants, conditions and agreements contained in the Lease, including, without
limitation, the payment of the fixed rent, additional rent and all other sums
then or thereafter due and to become due under the Lease.

                  (c) Assignee assumes the performance and observance of all of
the terms, covenants, conditions and agreements contained in the Lease,
including, without limitation, the payment of the fixed rent, additional rent
and all other sums due under the Lease; and

                  (d) The Landlord's consent as hereinabove set forth shall not
be construed as a consent by the Landlord to, or as permitting, any other or
further subletting or assignment by Tenant or Assignee.

            6. Upon Tenant's execution of this Agreement, Tenant shall, at its
expense, obtain and deliver to Landlord an amendment to the existing letter of
credit security deposit under the Lease (or at Tenant's option, a new letter of
credit), in either case, such amendment or new letter of credit shall, by its
terms, be transferable and shall name 345 Park Avenue South


                                       4
<PAGE>

Partners, LLC as the beneficiary thereof, and name ALM as the applicant thereof,
and shall state that the ultimate expiration date thereof is a date no earlier
than forty five (45) days after the Expiration Date.

            7. (a) Within sixty (60) days after this Second Supplemental
Agreement is fully executed and delivered to Tenant or its attorney, Tenant, at
its sole cost and expense, shall obtain all required governmental sign-offs and
approvals for all work, installations, additions and/or improvements heretofore
made by or for Tenant or any Tenant Entity in the premises demised under the
Lease (or any portion(s) thereof), including, without limitation the following:

            (1) Installation of Fire Alarm Speaker and Strobes - Installation
disapproved by Fire Department;

            (2) Installation of Fire Alarm, Speaker and Strobes, 7, 8 and 9 -
Installation disapproved by Fire Department; and

            (3) Addition to Fire Alarm - Additions disapproved by Fire
Department.

                  (b) Tenant hereby covenants and agrees that, subject to
Landlord's review and approval of final plans, drawings and specifications in
respect thereof as hereinafter more particularly set forth, Tenant shall
complete, at Tenant's own cost and expense and in a good and workmanlike manner
at least to the standard of Tenant's Work (as that term is defined in the
Lease), such permanent leasehold improvements and the permanent installations as
Tenant deems necessary for the use of the Remaining 9th Floor Portion as office
space (such work being hereinafter collectively called the "Remaining 9th Floor
Portion Work") and, subject to the provisions hereinafter set forth, Tenant may
make alterations, installations, additions and/or improvements in and to all or
any portion of the existing demised premises on the seventh (7th), eighth (8th)
and ninth (9th) floors (collectively, the "Existing 7th, 8th and 9th Floor
Work"). The Remaining 9th Floor Portion Work and the Existing 7th, 8th and 9th
Floor Work are hereinafter sometimes collectively referred to as the ("New
Work"). The New Work shall be performed in accordance with the provisions of
Article 6 and Sections 44.01, 44.02, 44.03 and 44.04 of the Lease except that
(i) the following provisions shall not apply to the New Work: (A) the last two
sentences of the second paragraph of Section 44.01; (B) the last sentence of the
third paragraph of Section 44.01; and (C) the provisions of subsections,
44.02(h), 44.02(j) and 44.02(k).

                  (c) If Tenant shall default in the performance of any of the
work set forth in subparagraph 7(a) above (after notice and upon expiration of
any applicable grace period, if any), then Landlord may perform such work on
behalf of Tenant, and if Landlord incurs any cost(s) in connection with
Landlord's performing such work, then Tenant will reimburse Landlord for such
cost(s), which cost(s) shall be deemed to be additional rent under the Lease (as
modified by this Agreement) and shall be paid to Tenant to Landlord within
twenty (20) days of rendition of any bill or statement to Tenant therefor.

                  (d) Provided Tenant shall have performed the Remaining 9th
Floor Portion Work as set forth in subparagraph 7(b) above, upon the completion
of such work and the delivery to Landlord of (A) executed and acknowledged
mechanic's lien waivers covering all


                                       5
<PAGE>

such work performed to date from all contractors, subcontractors, materialmen
and suppliers in respect of such work and (B) standard AIA Requisitions for
payment signed by a registered architect retained by Tenant at Tenant's expense
stating that all such work performed to date has been completed in accordance
with the Lease and applicable law, Landlord shall reimburse Tenant in an
aggregate amount equal to the lesser of (i) $164,280.00 or (ii) the actual cost
incurred by Tenant for the so-called "hard" construction costs for the
furnishing and installing the Remaining 9th Floor Portion Work, which
reimbursement (less ten (10%) percent for retainage) shall be paid to Tenant in
two (2) equal installments, the first (less retainage as aforesaid) when Tenant
has completed fifty (50%) percent of the Remaining 9th Floor Portion Work) and
the second (less retainage as aforesaid) when Tenant has completed the balance
of the Remaining 9th Floor Portion Work.

                  (e) Landlord shall not unreasonably withhold its consent to
the performance by Tenant of the non-structural portions of the New Work and
shall respond to all initial requests by Tenant for Landlord's approval of the
New Work within ten (10) business days following such requests by Tenant and
shall respond to all resubmissions thereof within three (3) calendar days
following such resubmission.

                  (f) Notwithstanding anything set forth herein to the contrary,
Tenant may perform cosmetic portions of the New Work prior to submission to
Landlord of plans and specifications for the New Work, provided the performance
of such cosmetic work is not then the subject of a comment or objection
previously raised by Landlord in writing with respect thereto, which comment or
objection is then unresolved, and, provided there is then no such unresolved
comment or objection, Landlord's consent for such cosmetic work shall not be
required.

                  (g) In the event of a dispute between Landlord and Tenant as
to the reasonableness of Landlord's disapproval of any portion(s) of the plans
and specifications for the New Work under circumstances where this Agreement
and/or the Lease specifically provides that Landlord's approval thereof shall
not be unreasonably withheld, such dispute shall be resolved by arbitration in
accordance with the provisions of Section 30.02(a) Article 38 of the Lease.

                  (h) Attached hereto as Exhibit B is a list of vendors approved
by Landlord for use by Tenant to perform the New Work and, provided Tenant uses
such approved vendors for the performance of the New Work, Landlord's approval
of such vendors to perform the New Work shall not be required.

            8. Provided Tenant has not theretofore been in default under any of
the terms and conditions of the Lease (as amended by this Second Supplemental
Agreement), Tenant shall receive an abatement of the fixed annual rent payable
in respect of the Remaining 9th Floor Portion in the sum of $32,856.00 per month
for the first (1st), second (2nd) and third (3rd) full calendar months of the
Adjustment Period for an aggregate abatement of $98,568.00. Notwithstanding the
foregoing, the Tenant shall be obligated to pay any and all additional rent,
electricity charges and all other sums and charges due pursuant to the Lease (as
amended by this Second Supplemental Agreement) for each of said months.


                                       6
<PAGE>

            9. Tenant shall have the option, exercisable on twenty (20) days'
written notice to Landlord, to elect to perform its own cleaning in and to all
(but not less than all) of the premises demised under the Lease, including the
removal of trash and rubbish therefrom, in which event Tenant, shall, at its
sole cost and expense, cause to be performed, by a union cleaning company
reasonably satisfactory to Landlord (or by an employee of Tenant) its own
cleaning and trash and rubbish removal in and to all(but not less than all) of
the premises demised under the Lease, and Landlord shall, upon the effective
date of such notice, thereafter have no further obligation to provide any
cleaning or trash or rubbish removal from the premises demised under the Lease
(or any portion(s) thereof) for and during the remainder of the term of the
Lease (or any renewals or exclusions thereof) and, upon such effective date, the
annual rental rate payable under the Lease shall for the then remainder of the
term of the Lease (and all renewals and/or extensions thereof), be reduced by
the sum of $66,174.00 per annum (the "Cleaning Rental Reduction").
Notwithstanding the foregoing, Landlord shall have the option, exercisable at
any time prior to the end of such twenty (20) day notice period, to cause the
Building's existing cleaning contractor to clean the premises demised under the
Lease in accordance with the then existing Building-standard cleaning
specifications, in which event Tenant's option to elect to perform its own
cleaning as aforesaid, and the Cleaning Rental Reduction, shall each be null and
void and of no force or effect and Tenant shall thereupon have no right or
option to elect to perform its own cleaning and/or trash or rubbish removal in
or to the premises demised under the Lease (or any portion(s) thereof), unless
Tenant reasonably demonstrates to Landlord that the cleaning of the premises
demised under the Lease (as amended by this Agreement) by Landlord's cleaning
contractor is substantially not in accordance with the cleaning specifications
which are applicable to this Lease (as amended by this Agreement) or that the
level of cleaning services being provided to Tenant in respect of the premises
demised under the Lease (as amended by this Agreement) are substantially less
than the level of cleaning services being provided to other tenants of similar
buildings in a similar geographic area.

            10. Subparagraph 11.02(a) of the Original Lease is hereby amended by
inserting the words "or to a subletting of up to seventy five (75%) percent of
the demised premises" after the word "Lease" on the second line of subparagraph
11.02(a) of the Original Lease.

            11. Landlord and Tenant covenant, represent and warrant to the other
that it has had no dealings or communications with any broker or agent other
than RFR Realty LLC ("RFR") [which is representing Landlord], and GVA Williams
a/k/a Williams Real Estate Co., Inc. ("Williams") [which is representing Tenant]
in connection with the consummation of this Second Supplemental Agreement and
the negotiation thereof, and each party hereto (the "Indemnifying Party")
covenants and agrees to pay, hold harmless and indemnify the other party (the
"Indemnified Party") from and against any and all costs, expense (including
attorneys' fees and disbursements) and liability for any compensation,
commissions and/or charges claimed against the Indemnified Party by any other
broker(s) or agent(s) claiming to have dealt with the Indemnifying Party.
Notwithstanding the foregoing, Landlord shall be responsible for any commission
or fee payable to RFR and Williams pursuant to a separate agreement(s) between
Landlord and RFR and Landlord and Williams and shall indemnify and hold Tenant
harmless in connection therewith. The provisions of this Paragraph shall survive
the expiration or earlier termination of the Lease.


                                       7
<PAGE>

            12.   (a) Pursuant to Section 31.02 of the Lease, all notices to
Landlord shall hereafter be sent to 345 Park Avenue South Partners LLC, c/o RFR
Holding LLC, 400 Park Avenue, 15th Floor, New York, New York 10022, attention:
Mark Granata.

                  (b) Section 31.03 of the Lease is hereby deleted in its entity
without substitution therefor.

                  (c) The reference to "James Finkelstein" in subparagraph 31.01
of the Original Lease is hereby deleted and the word "Attention: CEO" are hereby
inserted in this place and stead.

                  (d) Clause (A) of subsection (iii) of subparagraph 36.01(b)
is hereby deleted.

            13. Except as modified by this Second Supplemental Agreement, the
Lease and all covenants, agreements, terms and conditions thereof shall remain
in full force and effect and are hereby in all respects ratified and confirmed.

            14. The covenants, agreements, terms and conditions contained in
this Second Supplemental Agreement shall bind and inure to the benefit of the
parties hereto and their respective successors and, except as otherwise provided
in the Lease as hereby supplemented, their respective assigns.

            15. This Second Supplemental Agreement may not be changed or
terminated orally but only by an agreement in writing signed by the party
against which enforcement of any waiver, change, termination, modification or
discharge is sought.

            IN WITNESS WHEREOF, the parties hereto have executed this First
Supplemental Agreement as of the day and year first above written.

                                    LANDLORD:

                                    345 PARK AVENUE SOUTH PARTNERS LLC


                                    By:       /s/ Aby J. Rosen
                                        ---------------------------
                                               Aby J. Rosen, Member


                                    TENANT:

                                    THE NEW YORK LAW PUBLISHING COMPANY


                                    By:   /s/ William L. Pollak
                                        ---------------------------------
                                            William L. Pollak, President


                                       8
<PAGE>

                                  Tenant's Tax Identification Number is
                                  13-3273851.


                                  AMERICAN LAWYER MEDIA, INC.


                                  By: /s/ William L. Pollak
                                      ------------------------------------
                                      Name:
                                      Title:


                                  ALM's Tax Identification Number is 13-398-0414


                                       9
<PAGE>

STATE OF NEW YORK             )
                              )     ss.:
COUNTY OF NEW YORK            )

            On the _____ day of ____________ in the year 2000 before me, the
undersigned, a Notary Public in and for said State, personally appeared
______________________________, personally known to me or proved to me on the
basis of satisfactory evidence to be the individual(s) whose name(s) is (are)
subscribed to the within instrument and acknowledged to me that he/she/they
executed the same in his/her/their capacity(ies), and that by his/her/their
signature(s) on the instrument, the individual(s), or the person upon behalf of
which the individual(s) acted, executed the instrument.


                                   ---------------------------------------------


STATE OF NEW YORK             )
                              )     ss.:
COUNTY OF NEW YORK            )

            On the _____ day of ____________ in the year 2000 before me, the
undersigned, a Notary Public in and for said State, personally appeared
______________________________, personally known to me or proved to me on the
basis of satisfactory evidence to be the individual(s) whose name(s) is (are)
subscribed to the within instrument and acknowledged to me that he/she/they
executed the same in his/her/their capacity(ies), and that by his/her/their
signature(s) on the instrument, the individual(s), or the person upon behalf of
which the individual, s) acted, executed the instrument.


                                   ---------------------------------------------


STATE OF NEW YORK             )
                              )     ss.:
COUNTY OF NEW YORK            )

            On the _____ day of ____________ in the year 2000 before me, the
undersigned, a Notary Public in and for said State, personally appeared
______________________________, personally known to me or proved to me on the
basis of satisfactory evidence to be the individual(s) whose name(s) is (are)
subscribed to the within instrument and acknowledged to me that he/she/they
executed the same in his/her/their capacity(ies), and that by his/her/their
signature(s) on the instrument, the individual(s), or the person upon behalf of
which the individual, s) acted, executed the instrument.


                                   ---------------------------------------------
<PAGE>

                          APPROVED GENERAL CONTRACTORS
                              345 PARK AVENUE SOUTH


Theodore Williams Construction Company
345 Park Avenue
New York, NY  10154
Attn: Bart Caruso
      (212) 593-9700


NTX Interiors, Inc.
251 Park Avenue South
Suite 700
New York, N.Y. 10010
Attn: Robert Rudd
      (212) 780-2400


Tri-Star Construction Corp.
488 Madison Avenue
New York, N Y. 10022
Attn: William A. Wiener
(212) 486-0808