<PAGE>   1
 
                                                                      EXHIBIT 24
 
                               POWER OF ATTORNEY
 
KNOW ALL MEN BY THESE PRESENTS:
 
     WHEREAS, Lucent Technologies Inc., a Delaware corporation (hereinafter
referred to as the "Company"), proposes to file with the Securities and Exchange
Commission, under the provisions of the Securities Exchange Act of 1934, as
amended, a Form 10-K for the fiscal year ended September 30, 1998; and
 
     WHEREAS, the undersigned is a Director (and Officer) of the Company, as
indicated below following the signature:
 
     NOW, THEREFORE, the undersigned hereby constitutes and appoints Donald K.
Peterson and James S. Lusk and each of them, as attorneys for and in the name,
place and stead of the undersigned, and in the capacity of the undersigned as a
Director (and Officer) of the Company, to execute and file such Form 10-K and
any amendments or supplements thereto, hereby giving and granting to said
attorneys, and each of them, full power and authority to do and perform each and
every act and thing whatsoever requisite and necessary to be done in and about
the premises, as fully, to all intents and purposes, as the undersigned might or
could do if personally present at the doing thereof, hereby ratifying and
confirming all that said attorneys may or shall lawfully do, or cause to be
done, by virtue hereof.
 
     IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 16th day of December, 1998.
 
<TABLE>
<S>                                             <C>
          By /s/ RICHARD A. MCGINN                        By /s/ DONALD S. PERKINS
--------------------------------------------    --------------------------------------------
          Name: Richard A. McGinn                         Name: Donald S. Perkins
  Title:  Chairman of the Board and Chief                     Title:  Director
                 Executive Officer
 
           By /s/ PAUL A. ALLAIRE                         By /s/ HENRY B. SCHACHT
--------------------------------------------    --------------------------------------------
           Name: Paul A. Allaire                           Name: Henry B. Schacht
              Title:  Director                                Title:  Director
 
           By /s/ CARLA A. HILLS                         By /s/ FRANKLIN A. THOMAS
--------------------------------------------    --------------------------------------------
            Name: Carla A. Hills                          Name: Franklin A. Thomas
              Title:  Director                                Title:  Director
 
             By /s/ DREW LEWIS                              By /s/ JOHN A. YOUNG
--------------------------------------------    --------------------------------------------
              Name: Drew Lewis                              Name: John A. Young
              Title:  Director                                Title:  Director
 
           By /s/ PAUL H. O'NEILL
--------------------------------------------
           Name: Paul H. O'Neill
              Title:  Director
</TABLE>
<PAGE>   2
 
                                                                      EXHIBIT 24
 
                               POWER OF ATTORNEY
 
KNOW ALL MEN BY THESE PRESENTS:
 
     WHEREAS, Lucent Technologies Inc., a Delaware corporation (hereinafter
referred to as the "Company"), proposes to file with the Securities and Exchange
Commission, under the provisions of the Securities Exchange Act of 1934, as
amended, a Form 10-K for the fiscal year ended September 30, 1998; and
 
     WHEREAS, the undersigned is an Officer of the Company, as indicated below
following the signature:
 
     NOW, THEREFORE, the undersigned hereby constitutes and appoints Donald K.
Peterson as attorney for and in the name, place and stead of the undersigned,
and in the capacity of the undersigned as an Officer of the Company, to execute
and file such Form 10-K and any amendments or supplements thereto, hereby giving
and granting to said attorney, full power and authority to do and perform each
and every act and thing whatsoever requisite and necessary to be done in and
about the premises, as fully, to all intents and purposes, as the undersigned
might or could do if personally present at the doing thereof, hereby ratifying
and confirming all that said attorney may or shall lawfully do, or cause to be
done, by virtue hereof.
 
     IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 10th day of December, 1998.
 
                                          By:       /s/ JAMES S. LUSK
                                            ------------------------------------
                                            Name: James S. Lusk
                                            Title:  Vice President and
                                              Controller
<PAGE>   3
 
                                                                      EXHIBIT 24
 
                               POWER OF ATTORNEY
 
KNOW ALL MEN BY THESE PRESENTS:
 
     WHEREAS, Lucent Technologies Inc., a Delaware corporation (hereinafter
referred to as the "Company"), proposes to file with the Securities and Exchange
Commission, under the provisions of the Securities Exchange Act of 1934, as
amended, a Form 10-K for the fiscal year ended September 30, 1998; and
 
     WHEREAS, the undersigned is an Officer of the Company, as indicated below
following the signature:
 
     NOW, THEREFORE, the undersigned hereby constitutes and appoints James S.
Lusk as attorney for and in the name, place and stead of the undersigned, and in
the capacity of the undersigned as an Officer of the Company, to execute and
file such Form 10-K and any amendments or supplements thereto, hereby giving and
granting to said attorney, full power and authority to do and perform each and
every act and thing whatsoever requisite and necessary to be done in and about
the premises, as fully, to all intents and purposes, as the undersigned might or
could do if personally present at the doing thereof, hereby ratifying and
confirming all that said attorney may or shall lawfully do, or cause to be done,
by virtue hereof.
 
     IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney
this 10th day of December, 1998.
 
                                          By:    /s/ DONALD K. PETERSON
                                            ------------------------------------
                                            Name: Donald K. Peterson
                                            Title:  Executive Vice President and
                                                Chief Financial Officer