No problem. The letter designation signifies the load rating more than anything else. P tires are "passenger" with a 4 or 6 ply rating. LT tires (light truck) are 6, 8 or 10 ply rated.
Stiffer sidewalls, more capacity, but possibly harsher ride. P rated tires are used to give a better ride on a truck. LT tires have a higher min. and max. inflation rate. If a nice ride is important, you may lose some of it. It's not wise to run LT tires at the lower inflation weights of P tires. I did have a customer than put P tires on his 3/4 ton truck because they were cheaper. His low tire pressure light now stays on all the time. He can't safely inflate the P tires to enough pressure to put the light out. If you use LT tires you shouldn't have the tire pressure light problem. But you run the risk of having underinflated LT tires without knowing it.