As it happens, I've spent a lot of time over the last week talking to a guy in Romania who's trying to fix a sulfated lead-acid battery in his backyard garage. (I don't know if you've been to Romania, but the apocalypse happened 40 years ago there, so his available resources are kind of limited.) I think he's going to succeed, and may eventually progress to being able to recycle the lead into a new battery, but it's not going to be a weekend learning process or even a week-long one.
He reports that it's a "very complex electrochemical device".
The USPTO (?) has assigned the code H01M10/06 to lead-acid battery patents. https://patents.google.com/?q=(H01M10%2f06)&oq=(H01M10%2f06) finds 44'593 patents in this category. You don't need any of them to get a working lead-acid battery, but a significant subset of them are going to be helpful. Some are order-of-magnitude improvements.
And in a Mad-Max future (lots of cars around, but not enough fuel), there will be plenty of Lead Acid batteries laying around to recycle.
I do consider it effectively an apocalyptic kind of battery design. It was invented in the 1800s, its chemistry is incredibly simple (Sulfuric Acid + Lead), and is very well studied.
i prefer the phrase "anti-apocalyptic." Because by designing an energy efficient laptop/phone, less lithium/capacitor resources are manufactured and everyone can have one, unlike that single coke bottle in that 80s movie, "The Gods Must Be Crazy" which will lead to one. ;)
