Odds are, your vehicle did come with LT tires and the 225/75/16 were just the cheapest tire package offered, not the one people wanted if there was no cost difference.
The 4.3L wasn't very strong for the vehicle size (though not weak for that era, except hauling a load) but as others mentioned your rear diff ratio can help or hurt you loaded or unloaded, whichever your greatest need may be, EXECPT we are not talking about much difference here, not like the consideration is huge mudder tires weighing twice as much and 20% larger diameter!
If you never haul a significant load, and don't care how it looks, or rides, or ground clearance, get the cheaper, normally smaller tire, but the average non-base-model variant of the K1500 probably came with the 245/75/16 from the factory, and some had 265/75/16 from the factory, though "IMO" that is pushing it for handling on a 6.5" rim.
Ultimately I'd get the 245 again. It is a pickup truck and that seems like it has more virtues than detriments.