yeah, I knew I could dig around the php-lsapi code.
I think there "is not much interest" because it has never been published and documented. If somebody spent the time to properly document the API, then people would consider using it.
Given the benchmarks that nitewave just linked to, why would people not be interested in using it over fastcgi? Certainly if they are already litespeed clients, but perhaps promoting LSAPI for any application might result in new ones. It's a distinguishing feature that sets litespeed apart.
I personally think it would be worth litespeedstech's time to document it properly. I wouldn't think it would change much, so it should be a minimal effort to maintain once it was written. If it turns out nobody cares, it didn't cost much (a few hours time?), and it could potentially be very interesting to prospective clients.