<PAGE>
 
                                                                 EXHIBIT 10.8(b)
 
                              AMENDMENT NO. 1 TO
                                LEASE AGREEMENT

                                        
     THIS AMENDMENT NO. 1 TO LEASE AGREEMENT (this "Amendment") is entered into
as of June 5, 1997, by and between First Security Bank, National Association, a
national banking association, not in its individual capacity but solely as Owner
Trustee under that certain Trust Agreement, dated as of December 20, 1996, as
successor-in-interest to US Airways, Inc., formerly known as USAir, Inc.
("Lessor"), and Frontier Airlines, Inc., a Colorado corporation ("Lessee").

                               R E C I T A L S:

     A.  Lessor and Lessee have entered into the Lease Agreement, dated as of
July 26, 1994 (as amended, modified and supplemented to the date hereof and
hereby, the "Lease").  Capitalized terms used herein and not otherwise defined
shall have the meanings set forth or incorporated by reference in the Lease.

     B.  The Boeing Model 737-201 aircraft bearing manufacturer's serial no.
20212 was leased under the Lease pursuant to Lease Supplement No. 1, dated July
26, 1994 ("Lease Supplement No. 1").

     C.  The Boeing Model 737-201 aircraft bearing manufacturer's serial no.
19423 was leased under the Lease pursuant to Lease Supplement No. 2, dated July
26, 1994 ("Lease Supplement No. 2").

     D.  The Boeing Model 737-201 aircraft bearing manufacturer's serial no.
20214 was leased under the Lease pursuant to Lease Supplement No. 3, dated July
27, 1994 ("Lease Supplement No. 3").

     E.  The Boeing Model 737-201 aircraft bearing manufacturer's serial no.
19421 was leased under the Lease pursuant to Lease Supplement No. 4, dated
September 9, 1994 ("Lease Supplement No. 4").

     F.  The Boeing Model 737-201 aircraft bearing manufacturer's serial no.
20215 (together with the aircraft described in paragraphs (B) through (E), the
"Aircraft") was leased under the Lease pursuant to Lease Supplement No. 5, dated
October 4, 1994 ("Lease Supplement No. 5").

     G.  Lessor and Lessee desire to extend the Term of the Lease for each of
the Aircraft as hereinafter provided.



AMENDMENT NO.1 TO LEASE AGREEMENT                                         PAGE 1
<PAGE>
 
     H.  The Lease, together with Lease Supplement No. 1, Lease Supplement No. 2
and Lease Supplement No. 3 was recorded by the Federal Aviation Administration
on August 22, 1994 and assigned Conveyance No. EE007565.  Lease Supplement No. 4
was recorded by the Federal Aviation Administration on November 7, 1994 and
assigned Conveyance No. LL08354, and Lease Supplement No. 5 was recorded by the
Federal Aviation Administration on November 7, 1994 and assigned Conveyance No.
LL08355.

                                   AGREEMENT

     NOW, THEREFORE, in consideration of the foregoing premises and of the
mutual agreements herein contained, and for other good and valuable
consideration, the receipt and adequacy of which are hereby acknowledged, Lessor
and Lessee agree as follows:

     1.   Pursuant to Section 18.1 of the Lease, Lessee has notified Lessor that
Lessee has elected to extend the Term of the Lease for one Renewal Term with
respect to each of the Aircraft. Lessor and Lessee hereby confirm such
extensions, and agree that the Expiration Date of the Term, as extended by the
Renewal Term, for each Aircraft shall be as follows:

<TABLE> 
<CAPTION> 
             Manufacturer's        Expiration
             Serial Number         Date
             -------------         ----                  
             <S>                   <C> 
             N212US                July 26, 1999

             N207AU                July 26, 1999

             N214AU                July 27, 1999

             N205AU                September 9, 1999

             N217US                October 4, 1999
</TABLE> 


     2.   Lessee hereby confirms that it shall pay Basic Rent for each of the
Aircraft during such Renewal Term in accordance with Section 4.1 of the Lease.

     3.   Except as amended hereby, the Lease shall remain unmodified and in
full force and effect.


AMENDMENT NO.1 TO LEASE AGREEMENT                                         PAGE 2
<PAGE>
 
     4.   Lessee hereby represents and warrants that this Amendment has been
duly authorized by all necessary action and, assuming due authorization,
execution, and delivery thereof by Lessor, constitutes Lessee's valid and
binding obligation.

     5.   THIS AMENDMENT, INCLUDING ALL MATTERS OF CONSTRUCTION, VALIDITY AND
PERFORMANCE, SHALL IN ALL RESPECTS BE GOVERNED BY AND CONSTRUED IN ACCORDANCE
WITH THE LAWS OF THE STATE OF NEW YORK AS APPLICABLE TO CONTRACTS EXECUTED AND
DELIVERED IN SUCH STATE BY CITIZENS THEREOF TO BE PERFORMED WHOLLY WITHIN SUCH
STATE, WITHOUT REFERENCE TO ANY PRINCIPLES OF CONFLICT OF LAWS.

     6.   This Amendment may be executed by the parties hereto in separate
counterparts, each of which when so executed and delivered shall be an original,
but all such counterparts shall together constitute one and the same instrument.

                    [This space intentionally left blank.]


AMENDMENT NO.1 TO LEASE AGREEMENT                                         PAGE 3
<PAGE>
 
     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed as of the day and year first written above.

                                        FIRST SECURITY BANK, NATIONAL
                                        ASSOCIATION, not in its individual
                                        capacity but solely as Owner Trustee,
                                        as Lessor
                                        
                                        
                                        By:____________________________________
                                        
                                        Its:___________________________________
                                        
                                        
                                        
                                        FRONTIER AIRLINES, INC.,
                                        as Lessee
                                        
                                        
                                        By:____________________________________
                                        
                                        Its:___________________________________



AMENDMENT NO.1 TO LEASE AGREEMENT                                         PAGE 4