It is common for quarter ton, and even half ton pick-up trucks to be equipped with P-metric tires from the factory. The original equipment tires are always rated to carry the maximum load capacity of the vehicle. This means that from a load capacity perspective, P-metric tires are perfectly adequate. In fact, if you drive a pick-up truck or full-size SUV and rarely carry a load or go off pavement, then a p-metric tire will be a better choice for your replacement tire. They are typically less expensive, ride smoother, last longer, and are more fuel efficient than a LT-rated tire in the same size.
For pick-up truck owners that go off-road, routinely carry heavy loads, or tow a trailer, LT rated tires may be a better option. This is because LT tires have heavy cords and are more resistant to damage due to overloading or off-road conditions.
Putting LT tires on a vehicle that came with P-metric tires as original equipment is acceptable, but never replace original equipment LT tires with P-metric tires. This is because they have different load capacity ratings at recommended, and maximum air pressures, and the vehicle is designed for heavier duty use that may be beyond the capabilities of the lighter weight P-metric tire.