Typically lead-acid battteries are recycled as a whole unit. They're normally sent as universal wastes to a recycler who will typically resmelt the lead, recycle the plastic and neutralize the acid.
I'd contact your state's environmental agency to see if they know of local recyclers as well as if they have any additional requirements for generators.
Typical requirements are to keep the batteries upright (to prevent the acid from draining out), inspecting the batteries aren't leaking, and dealing with any spills/leaks of acid.
