Were you using php suexec when Apache is used?
Are you using PHP suEXEC with LiteSpeed? You can configure LiteSpeed to exactly match what you used with Apache. if mod_php was used, then turn off php suexec, if phpsuexec was used, then turn it on in LiteSpeed.
With phpsuexec, you need to change the file/directory ownership to "<user>:nobody" with permission mask 0750 or 0640.
without phpsuexec, you just change the permission mask to 0770 or 0660 with the ownership stay with "<user>:nobody". You should be able to switch between this two security models easily with command
"chmod -R g+w *" and "chmod -R g-w *"
That's just standard Unix file permission issue.