Rod does an experiment in permanently connecting a 12V Lead Acid and Lithium LiFePO4 battery together in parallel. It appears there could be synergies from the advantages of each battery. Sorry, it's a bit wordy. This experiment is now about 12 months old. No ill effects to either battery so far.

EV Power Australia Demo Video. Do try this at home but don't blame me if it does something bad to your hairdo.