I originally had a Freedom 15 xantrex inverter, a real primitive inverter. On the gel setting it kept the Lithium battery charged to 99% at all times. If I hooked up a lithium specific trickle charger I could get it to 100%. That worked fine for me for over a year until the inverting part of the inverter died. I didn't want to spend a fortune so I bought a older Xantrex 2000 XC and installed it. I also bought a new remote for it. The inverter did not have a lithium setting, but the remote did. Turns out that won't work. I then set them both to a user mode and set in the battery charging profile parameters. Works as advertised, but guess what still maintained 99%SOC just like the old gel setting.
Then I replaced my old solar panels with 2 - 100 watt panels and a victron 100/20 controller set to lithium. It also charges the Battery to 99% SOC.
All of that being said I suspect there is a setting on you inverter that will work the the lithium BIM to keep the battery properly charged. Try it before spending more money unless you just need a bigger inverter.