1. If you want to fully stuff the tire without rubbing the wheel well
then lift does not matter unless it's a drop bracket lift. A suspension lift will still have the tire traveling in the same space, it only changes where in that space it sits at rest. However if your truck never sees dirt
you can get away with a bigger tire with a lift and not rub (unless you hit a pothole or something).
is important for frame rubbing. Bigger tire (taller or wider) puts rubber farther away from the pivot point and closer to the frame when turned to full lock.
On my truck I am running 255/85R16 BFGoodrich KM2's on a 16x8 wheel with 4" backspacing. These are 33.3" tall tires. I have minimal rubbing here and there when fully (and I mean fully) stuffed. I used this guide for the most part to make them fit:
With no lift, if you follow the same steps and had the same tires/wheels as me, you would get the same results as me.
One important thing to watch is the actual tire size. Tire calculators will give you a rough diameter for a certain size tire but you should always check the actual specs of the tire. One size can vary almost an inch from brand to brand.
Now to specifically answer your question, I don't know 15" tire sizes and don't have time to look them up now. But you should be able to fit a 32" tire with no need to trim and no frame rub as long as you have enough backspacing. I ran 265/75R16 Cooper Discoverer STT's on the stock wheel (16x7 with 4.5" backspace) with a 1.5" spacer and it only slightly rubbed the frame at full lock. Same setup with Firestone Destination AT's and no rub. Also had the Firestones on the 16x8 wheels with 4" backspace and no rub.
If you want to fit a 33" tire, follow the steps in the guide I linked to and you'll be good. Other than centering the rear axle it took me maybe 30 minutes to do the trimming necessary.