It is likely caused by PHP crash.
You can add environment variable
LSAPI_ALLOW_CORE_DUMP
to lsphp5 external app configuration to let PHP dump a core file.
http://www.litespeedtech.com/php-litespeed-sapi.html
restart LSWS, then try the request causes 503 error, if core file produced under the same directory holding the script, then you can check the core file with GDB
gdb /usr/local/lsws/fcgi-bin/lsphp5 core_file_name
bt
It lists the stack call backs when PHP crashes, you can get some clue from it.