The chain will need relubrication at some point, just like any bicycle. We recommend a chain lube made for dry weather conditions, applied sparingly and excess wiped off to minimize mess in your home.
And also like any bicycle, we strongly advise against over-lubrication, which will attract dust / dirt which turns into a gritty paste and accelerates the wear of the entire drivetrain.
How often should you lube? Depends on how often you ride, but when the chain starts sounding “chirpy” it’s time to apply sparingly. I’m one of those fussy mechanics that will drip oil on each chain roller one at at a time. Others will blast a spray can of lube at the chain and saturate the chain, a rag, and everything else in spray’s blast radius. It’s your home, and we advise you go as minimal as possible.
While hot-waxing your chain is in vogue, and there are notable upsides in the context of indoor trainer bikes, HOWEVER - paraffin flakes off of waxed chains, and will end up all over your floor / rug / trainer mat. Again, you do you if this feels right.