I am not familiar with MATLAB's levinson function, but I presume it is part of one of their toolboxes and solves the symmetric positive-definite Toeplitz equation? If so, I am afraid that there are no routines in LAPACK specialized for such equations. Maybe a google search would reveal a suitable solver?
There was a paper "FORTRAN subroutines for general Toeplitz systems" published in TOMS by Per Christian Hansen and Tony Chan in 1992, with a corrigendum in 1994:
C ALGORITHM 729, COLLECTED ALGORITHMS FROM ACM.
C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
C VOL. 20, NO. 1, MARCH, 1994, P. 160.
The software is available from netlib, but, of course, it is in Fortran.