Where can I find mathematic models about batteries?
First of all, HOMER's battery module is not limited to lead-acid batteries. We suspect that some of its assumptions, such as the assumption of a fixed lifetime energy throughput regardless of depth of discharge, are more accurate for lead-acid batteries than for other kinds of batteries, but it is certainly possible to use it to model other kinds of batteries.
I think you are asking where to find the information you need to enter into HOMER's Create New Battery window. Unfortunately, I do not know of a single reference that contains that kind of information for many different batteries. In the past I have always relied on data from the manufacturer of the battery in question. If the manufacturer does not provide the lifetime curve, capacity curve, and other information on its website, I usually write to them to request further information.