xorlev, does the lsapi php binary dump errors in the logs when you execute it manually?
1) Stop litespeed.
2) /lswsinstall/fcgi-bin/lsphp -i [or name of your php binary with lsapi compiled and APC installed/configure in .../conf/php.ini]
Running the above command with -i or -v should get you basic info, confirm that APC is installed, and no error should be thrown to the logs.
Are you getting the 503s immediately for every php script execution on litespeed startup? Do the errors go away when you disable APC in php.ini?
Please give paste us the APC config/loading portion within your php.ini.
Also note when the php backened spawns processes to handel php requests, if APC is enabled with SHM (default), then you can check SHM allocation via "ipcs". There will be an entriy listed corresponding to every new php worker.