Here in the desert, the summer sun just destroys traditional lead-acid car batteries. In the car that we leave outside all year long, I'm very lucky to get two years out of a battery. The norm is about 18 months.It's absolutely not worth switching out the lead acid in the Model 3 for a lithium ion battery, IMO.
To the OP... It depends on how Tesla implements the new 12v lithium battery. If the battery itself has an onboard BMS system, and can handle the charging logic used to charge a 12v lead-acid battery, then it would most likely be OK. But if the 12v battery charging logic is handled by the car's computer, it wouldn't be OK, as our Model 3's don't have the capability to charge anything other than the OEM 12v lead-acid battery.
The currently available after market Lithium Iron Phosphate (or Lithium Ferrous Phosphate, if you prefer) batteries have their own onboard BMS system that deals with whatever voltage and current it gets (within reason), and distributes it to the battery cells appropriately. So these will work even in Model 3's, where the car thinks that it is charging a traditional lead-acid battery.
TL;DR If the new Tesla 12v lithium battery has its own BMS system and can handle lead-acid charging logic, it might work. If it does not have its own BMS, no, it won't work.