As others have said it depends on the converter... Generally a standard RV converter will never properly charge a LI battery but.. The problem is the word "Generally" some of them will fully charge them and some more than that.
Considering the cost of a good set of LI batteries and the cost of a replacement LI-Profiled Converter from Progressive Dynamics ... I'd upgrade the converter (But keep the old one just in cuss)
This one is $360 from Battle Born Batteries.. IF you search "Converter" on their web site you will find several other options
PD 4575 at BattleBorn