I have a 2016 JK. The lift is a fox/Mopar 2/4. Right now I have 35s/12.5 with 22”. Since those tires I added a stubby front bumper. Removed the inner liners. Added smaller flares. Will 37s fit now? I really can’t find any info...
As long as it's not overloaded with Groceries you should be ok, but in case you do get overloaded you can put air bags on the rear to raise the back up so the tires don't rub.
Also might add check to see how close the tires you have now come to rubbing when turned all the way side to side. You may have to put wheel spacers on.