I would not recommend a "P" (passenger) type tire for a pick-up truck hauling a load. That's what "LT" (Light Truck) tires are for. Basically a stiffer tire design, better suited to handling heavier loads. I think Walmart carries that size/type too.
Depends on the year of the truck, but I think the LT245/75R16 size was a standard tire for the 2500HD. The 18" and 20" wheels with low-profile tires were offered in some trim upgrades or as dealer add-ons for those who wanted a more stylish vehicle.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL