tire pressure monitor

If these are the external mount type, try moving that sensor to another tire and see if the same discrepancy happens with the replacement unit.

Sounds normal to me. I have run a tpms that shows temp for several years. Tires on the sunny side will be hotter. Tire closer to engine/exhaust heat will be hotter. Inner duals can be hotter due to less air circulation. And my right front toad tire runs considerably hotter (15+ degrees) than the other toad tires most likely because the big diesel exhaust dumps out right in front of it. All kinds of things can affect the tire temp, and therefore the psi also.

I don't have tpms but I do have a digital temperature monitor.
My first trip, the left side tires were 15 lbs higher. It took a minute to realize that the sun was shining on them.

Others will chime in but I think a few lbs one way or the other isn't a big deal.