Maybe this will help as I just recently replaced the battery in my GT.
The computer information that needs to be programmed includes the following (and, I'm guessing, it's the same in the i3):
- the capacity of the battery
- when it is installed (it appears to be an upcounter, so essentially, you reset it)
- the type of battery (it only showed wet lead-acid (conventional), and AGM types)
It's my understanding that it takes into account how old the battery is to determine how aggressively it can charge the battery and the actual charging voltage to best accommodate the type of the battery. In the case of the GT, there is a clutch on the alternator, and knowing the battery characteristics will help to determine when it actually turns on charging as opposed to more 'normal' cars that only rely on the battery voltage to alter the charging, and essentially are constantly holding it as close to full as possible. The advantage of an AGM type is that they are less likely to be damaged by a deeper discharge, so you can pick and choose when you want to charge it based on the current situation. In my GT, it normally only charges the battery when it is first started, but then later, only when you let off on the accelerator and then stops that process once you've stopped the car and are idling. That slight load can help decelerate the car, but can get twitchy unless they remove it just prior to you stopping so that last bit is smoother.
A Lithium based battery will have very different charge status logic than the types (I think) the car understands, so it probably would not last as long.
I've not looked in the area to estimate how easy it may be to find an alternate battery for the i3. Because BMW does appear to list a larger, alternate battery, it appears that it can be made to fit. They may actually have a different clamp or tray to accommodate that larger battery...just don't know. Others have indicated it doesn't fit without mods, but can't confirm.
Personally, I'd want an AGM battery in there. If you can find a larger one, that may be useful, but larger also means heavier and (maybe) more costly.
2011 535i x-drive GT, 2014 i3 BEV
Soon (hopefully!) A 2021 X5 45e will replace the above