What Rob said about your Converter is correct, however, I have heard that the new OEM Converters now come with switches for Lithium charging instead of the "Automatic" sensing. If your Converter has a switch, you should be fine using it, otherwise, I agree with Rob's recommendation about Progressive Dynamics.
Your other option is to not bother with replacing the OEM Converter and let your Solar system fully charge your Lithium battery. The way this would work is your OEM Converter would charge your battery to 60% - 80% and your Solar system would charge your battery up to 100%. Depending on your camping style and your energy storage needs, this option could serve you well for a few years.
As far as battery options:
I recommend you visit the thread "Affordable Solar..." pinned at the top of the "Solar and Generators" Forum on this website. In that thread, I recommend you read two of the links: first, "Cheap Batteries..." which discusses the newer value priced Lithium batteries. Second, "Cheap Batteries, Do You Have Them and Do You Like Them?", in this thread several people discuss their installation of these value priced batteries and how they like them (spoiler alert: they like them).
Additionally, I recommend you search the general Forum for: "Lithium Batteries, the Best Prices Yet" which I wrote a couple of days ago. In that post, I note that I found a 12v, 100ah, Lithium (LiFePo4) battery for the low price of $153 and several other brands for $173 (all with free shipping from Amazon).
When you are choosing a new Lithium battery(ies), I recommend you search YouTube for a teardown video of the battery brands you are considering purchasing to ensure that the battery meets your quality expectations.
Good luck and please let us know which batteries you choose and why.