First, the rule of thumb is that if you replace P type tires with LT type tires of the same dimensions, you need to add 15 psi to get the same load carrying capacity.
If you want to verify that, you need to find the tire load tables for each size. Since this is a Toyo bulletin, here are their load charts: Toyo Load and Inflation Tables
The key to this is that P type tires mounted on a light truck, SUV, or van have to have their load rating reduced by a factor of 1.1. So this becomes a math problem and the shortcut is to use the 15 psi rule of thumb!
And BTW, the load tables actually come from tire standardizing organizations. The one in the US is The Tire and Rim Association. They publish a book every year - about an inch thick - with all different kinds of tires (farm, mining, passenger car, trucks, etc.) including load tables and sizing standards. These load tables do not change from year to year because once published, they are used by tire manufacturers, vehicle manufacturers, and government regulatory agencies. So they have to be right the first time they publish them.
Also, P type tires come in SL (Standard Load) and XL (Extra Load). LT’s comes in Load Ranges (C, D, E, etc.)
And lastly - Why the difference in pressure? LT tires are made from a stiffer rubber than P type tires. That stiffer rubber tends to crack under more deflection, but is needed to prevent the rubber from flowing under the higher unit loading in LT tires.
Ya’ see, rubber is a viscoelastic material and does not behave like we normally think solids behave. Rubber will permanently deform under high shear stress, So rubber is tailored for its use and in some cases, made stiffer so cold flow is not an issue in the application. That is what goes on in the difference between P type tires and LT type tires.