question

if you have solar then leaving the inverter on while away should not be a issue and as such you could then use a lithium charger to charge to the level you require.

but then leaving a lithium set at say 50-70% for a few months or more, then the unit would not require any charging and thus why do you want a charger as they dont loose that much charge over a year if just left standing.

One thing comes to my mind. With agm batteries the voltage may get low but the air pump will stay running. With lithium the bms may at any time shut down the power.

LiFePo have a flat SOC curve, so targeting a particular SOC% in the midband will require hardware smarts (a coulomb counter on the charge/load path, integrated with the charger. And you may need to recalibrate from time to time). Easier to just target a (lower) float voltage.

For reference, BMS will also consume power. If you leave the battery connected to the BMS w/o a charging source for a long enough period you risk draining the battery to death unless the BMS cuts itself out of the loop.