Can I convert to Lithium "house" batteries in my Class C?

Can you convert yes.
What's involved
First you will need the new batteries
Second likely a new converter.... LiFePO4 has a slightly higher charge voltage
Finally you may need an electronic box between the engine/house isolator and the house... Basically a current limited DC/DC converter Depending on the vehicle (not house) electrical system... I think (Key word THINK not sure) GM alternators will work well with LI. not so sure about Ford or Chrysler.

If you have two 12 volt batteries in parallel going to a pair of GC-2 Flooded wet 6 volt in series might also help.. But I think the LI option is better.

I replaced my 2 lead acid batteries 4 years ago with a 170 AH Renogy lithium. I did not upgrade my converter which does not have a setting for lithium. The lead acid profile will not harm a lithium battery but it will not charge it fully. I did upgrade my solar charge controller to one that is suitable for lithium.

Check your converter it is new enough it may have a Li setting. I'm in the process of changing my 2018 Nexus 25P over to Lithium. I'm using a Renogy 40a DC-DC battery charger to charge the 2-200ah lithium batteries from the engine, my Zamp solar controller has a Li setting and I'm adding another solar panel. I'm still waiting on the 75a converter with Li setting from Best converters.

I'd do what Tom M has done--so long as no freezing cold weather is involved.

wa8yxm is the proper way to do it to get the maximum life out of your investment, yes you can do it like Tom_M did but make sure you turn off equalization on your charger if you have it, that can damage a LFP. The other reason I wouldn't do it this way is you are looking for more capacity by putting 400ah worth of lfp on a regular charger you're only getting your float voltage which is normally around 13.2 but can vary. This would give you a capacity of about 70% at the top end. since I don't recommend using the bottom 10% that leaves you with 60% of the capacity of the battery to use. and on two 200ah batteries that comes to about 240AH. If you put a proper charger in it and just pull the wires for the factory one, then you could use 80% of the capacity on a regular basis and 100% when you really need it. Using 100% will give you the rated cycle life, using 80% can increase that by a lot. 80% will give you 320AH to use on a regular basis and if that isn't enough you can fully charge to 100% and go till they are empty and get your 400.

the DC to DC charge is the same idea but rather to make sure you're getting a proper charging level off your alternator. I don't use one of these right now as I don't have any power from my truck going to the camper or the 5th wheel, only for the exterior driving lights. So, my solar charges when I drive. I am going to put one in though to act as an emergency backup. If you do charge from your alternator then you want one as your starting batteries have a different charge profile from LFP batteries and this allows you to charge your starting batteries properly and then go from that battery to the house batteries.

you could start out with just the batteries though and add the other stuff over time.

Stir

Tom finishes the charging using solar.

I love my dc to DC charger.

yup and if the OP had solar he could start like that also, or he can just take a reduction in capacity, or he can buy the right charger and a dc to dc charger and be good.