Back to your original question, which was, can I do it... Yes you can. You did not provide the loads you will be running while camping, but if you get by with two 80 amp/hr LA batteries, then one 100 amp/hour lithium battery will be enough.
With lithium you will have more available/useable amp/hours than with a lead acid, is almost a 2 to 1 ratio where 200 amp/hours of LA equals 100 amp/hrs of lithium. This is all based on USEABLE am/hrs, not total. You cannot use the last half of the LA battery basically.
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something like this works, or you can get a nicer one.
Is cheap and will tell you how much battery is left while u are camping.
The DC to DC charger is a must if you want to drive and charge.
If you dont want to upgrade your charger then you prob dont want to mess with solar, but 200 watts of solar go a long way to extend the battery on the trip. Indefinitely if you have sun, and importantly will end the need to recharge the battery , ever. With solar the battery/solar will recharge itself. You just park trailer and let it do the work. The idea of taking a battery out after a 4 day trip, lugging it in, hooking to a charger, then reinstalling it right before your next trip.... no. That kind of activity is better suited to the overly-expensive all-in-one battery "generators" that are made like luggage to be toted around..
Also, if you do not upgrade the converter, then if you ever camp with hookups, then you will have to still "boondock" power-wise as you cannot plug in and have the converter power the DC items because that includes charging the battery (putting current on the battery), unless you somehow separate the converter from the battery and at the same time separate the battery from all the DC devices so the converter powers DC yet is not connected to devices that are not connected to the battery. Way easier to just upgrade the converter or do something safe so you can have converter giving battery power. So, if you boondock at full hookups and want to run the air cond, then how you going to do that without pluggin in and without having converter power the lithium battery incorrectly?
Lithium is so much better than LA. Just jump in and do everything the right way from the start.