possible lightspeed sapi bug
 

When stracing PHP - I noticed:

unlink("2;/phpsessions/session_mm_litespeed0.sem") = -1 ENOENT (No such file or directory)
open("2;/phpsessions/session_mm_litespeed0.sem", O_RDWR|O_CREAT|O_EXCL, 0600) = -1 ENOENT (No such file or directory)
unlink("2;/phpsessions/session_mm_litespeed0.sem") = -1 ENOENT (No such file or directory)

We use the multi level feature of file based sessions which it appears that the litespeed SAPI can't handle.

Session handling is completely PHP internal feature, not directly related to any SAPI.
It is likely a problem with you PHP configuration.