I already tried to increase the Initial Request Timeout.
For what it matters, this error only happens after I enabled the "Flat Catalog Category" feature on a Magento site if you are familiar with it. The CPU of the lsphp5 process stays on 100% and then the application crashes after 30-40 seconds with 503 error. No other error in stderr.log.
I already contacted CloudLinux and they say it is a Litespeed issue.