Some LMS providers are now trying to include these. But this will be a point of contention as we move forwarded. You will probably find that some will try to be the ERP of human capital. But, examine what information you have to keep confidential and what you don't. Nothing is foolproof.
Big issue is demonstration of very secure environment, redundancy, up-times.
The data LMS keeps within it, is a very small subset of the HRIS system. This relaxes people. Content can reside anywhere. It can be pointed to, launched, tracked from another server. A lot of these decisions are driven from large organizations that are global that can't track there charge backs, discounting, transfers, etc.