Thank you for trying our web server.
By default, PHP looks for MySQL's socket at /tmp/mysql.sock, it is configurable in php.ini. RedHat usually place MySQL's socket somewhere else, see your /etc/my.cnf. Both configuration should match.
Your problem may caused by the missing php.ini if you are using the prebuilt PHP binary coming with our installation package, it is configured to search php.ini under ../conf/ instead of /usr/local/lib/. One quick solution is to copy /usr/local/lib/php.ini to [lsws_home]/conf, restart server or just kill all PHP processes.
Only FastCGI interface is enabled in the prebuilt PHP binary, so if you need any features that are missing, you need to build PHP from source, for detail, please read respective HOWTO. Please stay with 4.3.1 if you can, as newer versions are bugy in fast CGI interface.
If your site is database and/or PHP script intensive, you may not observe big performance boost by switching to our server unless it is under extreme load, Apache could become really slow. If you want you can run both web servers on different ports in parallel and "ab" them. You also can try PHP Accelerator see if it help.
We'd like to know how is our web server against Apache, please post your impression if possible.