Do you host your customer's on the same server? if so, its good to have LiteSpeed onboard as it can bring in noticeable improvements to your client's websites. There must be some solution as these solutions are stable and running for years! Did you contact litespeed support regarding this? if your support company cannot resolve the issue, you may contact litespeed support team and they can help you.
Litespeed is very good. It has been around for ages now, and widely used. Makes a big difference to the performance of sites. They should be able to help you resolve the issue. I would find it unusual if they can't.
We use it for hosting, and we use it alongside Whmcs and works without any issues.