<PAGE>   1
                                                                    EXHIBIT 10.4

                            EIGHTH AMENDMENT TO LEASE

        THIS EIGHTH AMENDMENT TO LEASE (hereafter "Eighth Amendment") is made
and entered into this 31st day of May, 2001, by and between WALTON SEATTLE
INVESTORS I, L.L.C., a Delaware limited liability company as Landlord, and N2H2,
INC., a Washington corporation, as Tenant.

                                    RECITALS

        A. Landlord and Tenant have entered into that certain Office Lease dated
March 12, 1999, as amended by the First Amendment to Lease dated June 16, 1999,
the Second Amendment to Lease dated August 10, 1999, and the Third Amendment to
Lease dated August 12, 1999, the Fourth Amendment to Lease dated October 12,
1999, the Fifth Amendment to Lease dated February 14, 2000, and Sixth Amendment
to Lease dated April 4, 2000,Seventh Amendment to Lease dated December 14, 2000
(as amended, the "Lease"), whereby Landlord has leased to Tenant and Tenant has
leased from Landlord approximately 55,887 rentable square feet, known as Suite
3400 ("Initial Premises"), in that certain building located at 900 Fourth
Avenue, Seattle, Washington 98164 ("Building").

        B. Landlord and Tenant desire to further amend certain terms and
conditions of the Lease whereby Tenant shall surrender possession of the space
known as Suite 3350 constituting approximately 4,255 rentable square feet on the
33rd floor as highlighted on attached Exhibit A-1 ("33rd Floor Premises") and be
released from the obligations pertaining thereto as more fully set forth in this
Eighth Amendment.

        C. All capitalized terms not otherwise defined herein shall have the
same meaning as set forth in the Lease.

        NOW, THEREFORE, in consideration of the mutual covenants and conditions
stated herein, Landlord and Tenant hereby modify, amend and supplement the Lease
and agree as follows:

1.   SPACE REDUCTION DATE. The surrender date of the 33rd floor Premises (as
     defined below) shall be midnight, June 30, 2001 (the "Space Reduction
     Date") so long as the Condition set forth in Section 6 is met. Prior to the
     Space Reduction Date, Landlord shall have unrestricted access to the 33rd
     Floor Premises for the purposes of preparing such space for occupancy by
     another tenant.

2.   PREMISES. On the Space Reduction Date, Tenant shall unconditionally and
     irrevocably surrender to Landlord and Landlord shall retake possession from
     Tenant of the 33rd Floor Premises. From and after the Space Reduction Date,
     the 33rd Floor Premises shall be subtracted and hereby excluded from the
     definition of Initial Premises, which, from and after the Space Reduction
     Date shall constitute a total of 38,724 rentable square feet, as more
     particularly shown on Exhibit A-2.

3.   RELEASE. From and after the Space Reduction Date, Tenant shall release
     Landlord and Landlord's partners, officers, directors, agents, employees,
     successors, assigns, property manager and contractors from each and every
     claim of every type and nature arising from the Lease as it relates to the
     33rd Floor Premises, Tenant's occupancy of the 33rd Floor Premises, and the
     relationship of Landlord and Tenant as landlord and tenant under the Lease
     relating to the 33rd Floor Premises excepting only any claims relating to
     or arising out of obligations of Landlord which, pursuant to the Lease,
     survive the expiration or earlier termination of the Lease. From and after
     the Space Reduction Date, Landlord shall release Tenant and Tenant's
     respective partners, officers, directors, agents, employees, successors,
     assigns and contractors from each and every claim of every type and nature
     arising from the Lease as it relates to the 33rd Floor Premises, Tenant's
     occupancy of the 33rd Floor Premises, and the relationship of Landlord and
     Tenant as landlord and tenant under the Lease relating to the 33rd Floor
     Premises, excepting only any claims relating to or arising out of any
     obligations of Tenant, which pursuant to the Lease, survive the expiration
     or earlier termination of the Lease. The foregoing releases shall not apply
     to claims or causes of action arising from or in connection with the
     enforcement or interpretation of the rights and obligations of the parties
     under this Agreement.

4.   BASE RENT: Section 1.l) of the Lease shall be replaced in its entirety with
     the following: .....................................

<TABLE>
<S>                                                                                 <C>
     Rent Schedule:.................................................................Total Base Rent
     Space Reduction Date through 12/31/01:.........................................$96,719.98
     01/01/02 through 12/31/02:.....................................................$99,946.97
     01/01/03 through 12/31/03:.....................................................$103,173.98
     01/01/04 through 11/30/04:.....................................................$106,251.92
     12/01/04 through 04/30/05:.....................................................$110,462.95
</TABLE>


                                       1
<PAGE>   2
<Table>
<S>                                                                                 <C>
     05/01/05 through 08/31/05:.....................................................$110,154.15
</Table>

5.   RENT CREDIT: So long as Tenant is not in default of the Lease, Tenant shall
     receive a rent credit of $500.00 per month ("Rent Credit"). The Rent Credit
     shall commence with the first payment of Rent due after such time as the
     Rent Credit which otherwise would have been earned by Tenant has been
     applied to cover all legal fees incurred by Landlord with respect to this
     Amendment or the reletting of the 33rd Floor Premises For example, if
     Landlord incurs legal fees of $2,000 with respect to this Amendment and the
     reletting of the 33rd Floor Premises, then the Rent Credit shall commence
     on September 1, 2001 (four months of Credit at $500 per month).

6.   CONDITION. This Amendment is conditioned upon Landlord and Verio, Inc.
     executing a lease agreement for the 33rd Floor Premises prior to the Space
     Reduction Date.

7.   PARKING: Section 1.q) is hereby replaced with the following:

     Thirty-five (35) unreserved stalls at the prevailing market rate.

8.   ENTIRE AGREEMENT. This Agreement represents the entire understanding
     between the parties hereto with respect to the partial termination of the
     Lease. This Agreement shall not be modified by either party by oral
     representation made before or after the execution of this Agreement, and
     all modifications shall be in writing signed by the party against whom
     enforcement of such modification is to be sought.

9.   NO CONFLICT. Except as modified by this Eighth Amendment, the terms and
     conditions of the Lease shall remain in full force and effect. In the event
     of any conflict between the terms of this Eighth Amendment and the Lease,
     this Eighth Amendment shall govern and control the intent and agreement of
     the parties.

IN WITNESS WHEREOF, the parties hereto have executed this Eighth Amendment to
Lease as of the date first set forth above.

LANDLORD:

WALTON SEATTLE INVESTORS I, L.L.C.,
a Delaware limited liability company

            By:  Walton Street Real Estate Fund I, L.P.,
                 a Delaware limited partnership,
                 Manager

                 By:  Walton Street Managers I, L.P.,
                      a Delaware limited partnership,
                      General Partner

                      By:  WSC Managers I, Inc.,
                           a Delaware corporation,
                           General Partner

                           By:  /s/ Douglas J. Welker
                                ---------------------
                                Douglas J. Welker,
                                Vice-President


TENANT:

N2H2, INC.,
a Washington corporation, as Tenant.





By:  /s/ J. Paul Quinn
     --------------------------
     J. Paul Quinn,
     CFO


                                       2
<PAGE>   3

                                   NOTARY PAGE

STATE OF ILLINOIS            )
                             )      :ss.
COUNTY OF COOK               )

I certify that I know or have satisfactory evidence that the person appearing
before me and making this acknowledgment is the person whose true signature
appears on this document.

On this ___ day of March, 2001, before me personally appeared DOUGLAS J. WELKER,
to me known to be the VICE PRESIDENT of WSC MANAGERS I, INC., a Delaware
corporation, the corporation that executed the within and foregoing instrument
as GENERAL PARTNER of WALTON STREET MANAGERS I, L.P., a Delaware limited
partnership, the GENERAL PARTNER of WALTON STREET REAL ESTATE FUND I, L.P., a
Delaware limited partnership, the MANAGER of WALTON SEATTLE INVESTORS I, L.L.C.,
a Delaware limited liability company, the company joint venture that executed
the within and foregoing instrument, and acknowledged the said instrument to be
the free and voluntary act and deed of said joint venture, for the uses and
purposes therein mentioned, and on oath stated that he/she was authorized to
execute said instrument.

WITNESS my hand and seal hereto affixed the day and year first above written.


                               ----------------------------------------
                                      LA DUKE
                               ----------------------------------------
                               [Type or Print Name]

                               Notary Public in and for the State of Illinois,
                               residing at Chicago, IL
                                          --------------------------- .
                               My Appointment Expires:  9-05-04
                                                      --------------- .




STATE OF WASHINGTON        )
                           )      :ss.
COUNTY OF KING             )

On this ___ day of March, 2001, before me personally appeared J. PAUL QUINN to
me known to be the CFO of N2H2, INC., the corporation that executed the within
and foregoing instrument, and acknowledged the said instrument to be the free
and voluntary act and deed of said corporation, for the uses and purposes
therein mentioned, and on oath stated that he/she was authorized to execute the
said instrument and that the seal affixed, if any, is the corporate seal of said
corporation.

IN WITNESS, WHEREOF, I have hereunto set my hand and affixed my official seal
the day and year first above written.



                               ----------------------------------------
                                    Janis Boucher
                               ----------------------------------------
                               [Type or Print Name]

                               Notary Public in and for the State of Washington,
                               residing at Bethell, WA
                                          --------------------------- .
                               My Appointment Expires:  1-28-04
                                                      --------------- .


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<PAGE>   4

                                   EXHIBIT A-1

                               33RD FLOOR PREMISES

                (Floor plans showing Recaptured Premises shaded)




                                    [GRAPHIC]




(c)NORTH                                                           *NOT TO SCALE


                                       4
<PAGE>   5

                                   EXHIBIT A-2

                                    PREMISES

                                   34TH FLOOR

                      (Floor plans showing Premises shaded)





                                    [GRAPHIC]




(c)NORTH                                                           *NOT TO SCALE



                                    PREMISES

                                   35TH FLOOR

                      (Floor plans showing Premises shaded)





                                    [GRAPHIC]




(c)NORTH                                                           *NOT TO SCALE


                                       5
<PAGE>   6

                             EXHIBIT A-2 (CONTINUED)

                                    PREMISES

                                   36TH FLOOR

                      (Floor plans showing Premises shaded)





                                    [GRAPHIC]




(c)NORTH                                                           *NOT TO SCALE


                                       6