No, it is not possible to run the ESRI License Manager on Linux.
The ESRI License Manager is supported on the following platforms:
Windows - XP, 2000 and NT 4.0 SP6a.
UNIX - Solaris 7, 8, 9 & 10, HP 11, TRU64 5.0 & 5.1, IRIX 6.5.6 and 6.5.9, and AIX 184.108.40.206 and 5.1.
For details about System Requirements, see the link in the Related Information section below.