Not sure how anybody but you could determine if your camper has an inverter.
If you can use any 120VAC devices without being plugged into shore power or a generator, you have an inverter. Otherwise, you don't.
You'll need to check the model of your unit's charger/converter. If it bulks to 14.2-14.6V, absorbs 13.8-14.6V and floats at 13.2-13.6V, it should be fine for the most part. The bigger issues with RV is the garbage wiring between the converter and the battery. It often causes a big voltage drop that mucks up charging. In shore power charging cases, it rarely matters since you're not worried about fast charging, but if charging with a generator, it can increase generator run times significantly.
If you're going to go boondocking frequently, LFP is a great option. If you're only going to take it out once a month, spend most of the time on shore power, etc., then LFP is not worth the cost unless you're looking for lighter weight/smaller volume.
LFP bad choice for:
Infrequent cycling
Backup power where backup events are infrequent.
Starting generators, engines.
Things that use may use greater than 100A of current, even for brief periods (coffee maker, microwave, etc.).
If you have money to burn, or you're a slave to keeping up with the Jones', and you know what you're getting into, go for it.