It appears your shore charger is a Tripp-lite RV1512UL inverter/charger which basically only has a Gel & Wet cell setting. This would make this a good choice to be replaced with a unit that supports a lithium and/or programmable charge settings.
I would expect that your that your build uses a Blue Sea ACR for the alternator to house charging. So you also would need to look for a new solution for alternator charging of the house battery.
Now I would start looking at lithium batteries and decide which manufacturer that you are interested in going with. This is important as each manufacturer should have the settings that they want for their battery. This way when you look for new charging devices that will meet the the charging parameters of the battery you go with.
Now when choosing a lithium battery you have another specification to be worried about. Many of the internal BMS batteries, are limited in current discharge by the size of the internal FET's used to protect the lithium batteries. This many times is specified around 100 amps. So if choosing a 100 Ah battery you might have a discharge capability 100 amps continuous (200 Amp Surge). This becomes important if you are a big inverter uses as it will be your largest current user. 2000 watt / 12 volts = 167 amps. This would mean that you would need two 100 Ah batteries in parallel to use your inverter to full capacity. So check your choices and make sure you can support your chosen system. If you choose a external BMS you will need to check that specification also.
For the alternator charging you will have to change the ACR solution. A common solution is a DC to DC charger, like Sterling Power or KISAE DMT1250. There are many more on the market and it is growing. This will enable you to take alternator power and charge your lithium battery with the correct parameters for the battery.
A simpler solution would be much like your ACR, but has additional capabilities like Precision Circuits Inc LI-BIM or Battery Isolation Manager. The BIM limits the charging of the lithium battery to around 80% to prevent over charging. Take this into account in your power usage calculations.
If moving to a large lithium bank a second alternator with a multi-stage regulator would be a better choice.
Most solar controllers also now support lithium but again, you want to make sure that they support the battery of your choice. Some of the DC to DC chargers available have a solar input also, making one unit for both solar and alternator charging.
I do cover some of these devices in the Battery Isolators, Separators, Switches & More (updated 2020)
post starting on post #5
Many Inverter/Chargers now support lithium. I will throw in a shameless plug for a New in the Box Magnum MS2000
I have available.
hope this helps.