This morning I shut down litespeed and lsapi, and rebuilt lighttpd with their new version 1.4.15 which happily fixed the 500 errors.
So when I got your PM, I re-enabled litespeed and lsapi. The PHP functionality is now working. I can't explain why other than perhaps it was a browser caching issue. I did definitely restart the server hard.
The SSL is not working though. The same exact SSL certifications are working fine with lighttpd, so that is not the culprit.
Also, the "graceful reboot" doesn't seem to work. It just hangs. I will just restart it from the command line I guess.
I'll send a PM so you can take a look at the ssl issue.