I could be wrong (since I donít own a rapid camp system), but I suspect Lippert will say the battery cannot be replaced and you may be forced to purchase a replacement remote. You could try calling them first to confirm that no battery replacement is possible.
There is a video on Utube describing how one person used a modified USB cable and USB remote battery pack (5VDC) to hard wire to the old battery terminals in their rapid camp remote control.......but it may not be the unit you have; and may not be a very convenient or appealing solution for many folks.
If you confirm that battery replacement is not possible from Lippert officially, then if it were mine I would check for any screws in the rear of the remote (may be obvious; may be under rubber feet; may be under glue on tags). If no screws are used to hold the remote halves together, then you may have to carefully pry open the case with a pocket knife or thin plastic tools intended for that kind of purpose. Once inside, see if you can identify the battery part number/manufacturer and see if you can find a similar item on eBay/Amazon (physical size and voltage) etc. An example of a 3.7vdc rechargeable battery for a dash cam, on eBay, is attached FYI......but you would need to match your remote battery voltage specs etc. and may have to adapt, solder wires etc. Good luck.