It is definitely possible to use a Lithium battery, and with prices coming down quickly you might want to go in that direction given all their advantages. I removed the Westfalia charging system altogether and installed a dedicated DC-DC battery charger that also allows solar panel inputs. (uses solar when there is enough power available from them).
Choosing a battery (probably hundreds out there now), you will have to make sure of a few things:
1 ) the BMS (battery management system) on the battery itself must protect against the usual stuff - High current drain, low voltage/high voltage cutoff, high battery temperature etc.. Most lithium batteries on the market now have all that... BUT they don't all have LOW temperature protection (that is usually available for an additional $200 or so). Lithium batteries are damaged if you attempt to charge them when they are below 0 deg C (32 F). If you never see that cold, then don't worry about it. Some offer heating systems to enable the battery use in winter.
2) You need a DC-DC charger system to allow safe charging from your vehicle alternator/main battery or a solar system. The charger will effectively limit the current drain from your main to something reasonable like 30A, and as well to stop stealing power from the main battery when the available voltage is getting too low. You seriously NEED this to protect your main battery. If you try to drop the Li battery in without it, it will draw too much power and overload your alternator and possibly burn up some important wiring! Here is an example of a good DC-DC charger system:
Renogy 30A MPPT DC to DC Battery Charger 12V Car Battery Charger On-Board Charger
You should also add an in-line fuse between your alternator and the charger just to be absolutely safe.
Many Li batteries also have a bluetooth output that allows you to see what is going on (%charge, current draw, voltage, temperature etc) from your smartphone. That is a nice option for real geeks like me.
Unfortunately you will have to give up on some of the functionality of the Westfalia charging system. I can only see the battery voltage on the overhead panel now.