My understanding, mod_php/phpSuExec/suPHP are 3 different apache modules.
in which, mod_php has best performance, suPHP is slowest since it run as CGI.
lsphp is php with LSAPI to work with litespeed web server. It can run as global user/group(e.g. nobody) which is like mod_php, also it can run in suExec mode as user's privilege. and they can run at the same time --- some lsphp processes run as global user, while some lsphp processes run in suExec mode.
We did some bechmark tests regarding various PHP a few months back, and posted the result on our blog:
Litespeed is apache interchangeable. however, you need rebuild php with LSAPI to work with litespeed. custom php.ini should work as before and no need change, or minimum change only -- for example, the php extension's directory.