Thanks Boots, yes...that's what I have read too. So if I were to use a regular AGM battery charger in lieu of a Lithium compatible charger it could not be left to "maintain" the battery.
The J35B BMPRO I have does not have the ability to revive a highly discharged battery...so it seems there is no desulphation program. From the manual: "If a battery has become deeply discharged though, the J35 will not charge it. Remove the battery and charge it with a stand-alone charger. Once the battery voltage has recovered to normal levels, it may be reinstalled."
It does though have the "boost" mode where it will kick in moments of high voltage to maintain the battery cell levels. This would not be good for any lithium battery.
"J35 is a full battery management system with a multi-stage battery charger including bulk, absorption, float, and periodic boost charging modes to ensure long battery life."
Realistically then, Lithium batteries would be fine with the J35B distributing power...but, would risk damaging the batteries if for example in a Park on a powered site as the BMPRO would be charging the batteries constantly, and potentially enter in to the phase where it would send pulses of high voltage to the batteries...
So off grid would be fine as the charge input would be from solar panels through a Lithium compatible MPPT regulator...
Interesting article;
https://www.power-sonic.com/blog/can-i-charge-a-lithium-battery-with-a-normal-sla-charger/