Idling is not good. Better take if for a ride.
My van can stand for 2 - 3 months and a 3 years old good quality starter's battery has no problem keeping the voltage around 12,6 V (checked lately, it was standing since beginning of September when I drove 70 km until two weeks ago when I made a short trip to pick up the solars).
As far as I remember, I've read somewher (here or on some MH forum) that there was a charger that could charge both lead-acid and Lithium, that could be a solution for you. I think it was something from Victron. I've just checked and CTEK also has this type of charger for lead-acid and LiFePO4 batteries. It's the model 40-330, it's 8 A, so would be slightly too small for your 100 Ah starter battery (but should do). Before investing check with the dealer what type of Lithium battery you have.
Charging current for lead-acid batteries should be 0,1 of the capacity in order to assure proper charge, so I'd look for a 10 A charger. Of course you can use a smaller one, but it'd be impossible to charge it properly if the battery gets flat for some reason in the future. And of course will take longer to charge.