Batteries aren't a good source of lead because most of the lead is in the form of lead oxide, lead dioxide and lead sulfate. The most lead you will get out is a couple pounds from the battery posts, bus bars and some from the grids.
To get most of the remaining lead, there are two methods, blast furnace (not just heat, because the sulfate need to be reduced, so the furnace needs coke or fuel for the carbon to react with the oxides to convert the lead oxides to lead, plus excess air supply to burn off/reduce the oxides and carbon), or electrolysis. Both methods it needs to be ground up with the remaining paste. One into the blast furnace the other way into concentrated sodium hydroxide solution and the lead removed by electrolysis. Also, with a blast furnace, if the fumes aren't captured and treated, you will contaminate your property, and everything for miles downwind.
You then have lead, but also a huge amount of everything that remains behind, goo, or slag. An industrial process further separates and treats the mess, and recycles most of it. But in your backyard? Not so much......
Spot lead market prices are now around 90 - 95 cents a pound. So might be able to get some for a reasonable cost from a large supplier.