I have 2" steel coil spacers on my '01 2500. You can 'fit' LT315s on your truck.
I am running LT285s right now on the stock 16x8 (6.5" backspacing) forged aluminum rims. I have a ton of room and no rubbing issues.
I also ran LT315 Dunlop Radial Mud Rovers for about a year. I would not even consider running these tires without aftermarket rims, with less backspacing. I used Weld Racing Scorpio rims, 16x8 with 4.5" of backpacing. With the 2" spacers, the LT315 sized tire looked great and really peformed off road.
The LT315s are alot bigger tire than the stock LT265s, and are even a lot bigger than the LT285, that I am currently running.