Many driv
ers understand it's important to monitor the air pressure in their tires. Improperly inflated tires hurt fuel economy and cause irregular and/or rapid tire wear in addition to posing safety problems.
It's recommend to check your tires' pressure at least once a month and before any long trip. Who really marks their calendar each month with a reminder to check tire pressure? I'll plead guilty that I don't. Instead, I check mine each time I wash my car.
You've got your air pressure gauge in hand and air compressor ready, but some will ask, "How much air pressure should I have in my tires?" Logic might dictate that one would simply check the sidewall of the tire, much like you do on a bicycle tire. However, this would be incorrect. The tire size used on your vehicle is also used on other vehicles and the recommended air pressure is different depending on the vehicle. For example, it may surprise many that a 2006 Acura MDX SUV uses the exact same tire size as a 2010 Chrysler 300 sedan.
Remember that the pressure listed on the sidewall is a maximum pressure only, not a recommended pressure. Instead, use the air pressure recommended in the vehicle's owner's manual or tire information placard label. The placard is typically found in the driver's side doorjamb, like the example in the photo above.
For more information on properly setting your tire pressure, read "Checking Tire Inflation Pressure."

Your setups have sizes that we haven't tried so the following are my best guesses on what ranges I would start the air pressure at :
98 Lexus GS400 34-36psi
97 Caidillac DVille 32-34psi
07 Lincoln Navigator 35-36psi 42psi with passengers/luggage/cargo
We do not carry Hercules tires, nor have we tried this size on a Jeep so I do not have information on a tire pressure for this application.
These tires sizes will also use the same air pressures front and rear as your factory 18" sizes as the same overall diameter has been maintained for proper tire load capacity.