There are good reasons to go Li-Ion rather than lead acid. First of all, remember that most applications that use lead acid batteries use LiFePO4 chemistry when converted to lithium (rather than the LiCo or LiMn chemistries more typical of flashlights). LiFePO4 batteries are EXTREMELY robust compared to lead acid (and other lithium chemistries). They can endure 2000+ charge and discharge cycles - more than lead acid or other lithium ion batteries. And, unlike lead acid, the battery won't die from sulfation if left in a partially charged state. LiFePO4 actually likes a partially discharged state, but (unlike other lithium chemistries) is okay with being fully charged for long periods, too. So LiFePO4 may be a good way to go simply because the battery will last ALOT longer. Finally, one of the very best features of LiFePO4 is its ability to maintain a practically constant voltage throughout discharge - even more so than NiMH. This means that the battery does not tend to run down with use. It remains strong until dead. For all these reasons, I would seriously consider going LiFePO4 rather than lead acid.
As for wiring up a generic LiFePO4 cell rather than getting the proprietary battery, this may be possible. LiFePO4 has very similar charging characteristics to lead acid. The voltages are very similar. And they both use constant current/constant voltage charging. LiFePO4 often does employ a specific battery management system. But this is often employed in the battery itself for retrofit applications (like automotive use). Beware, though. It may not be possible to simply replace the existing lead acid batteries for other reasons. And it would almost certainly void the warranty. You might actually want to pony up for the proprietary batteries.