On a lawn tractor, there are lots of variables but nothing comparable to what you need for a CUT or even a big ag tractor. If 7 pounds seems comfortable to you and the tire is not slipping on the rim, then I wouldn't change a thing. I run about 12 PSI on my zero turn mower which weighs 850#.
What you want to do is put just enough air to have the full bar tread contacting the ground. This may not be possible with your lawn tractor with the larger than factory tires, the sidewalls may be so stiff that they wont make full contact even with 0 psi in them. In that case, 7-10 PSI would be my range of operation for them. Even on my 70 HP tractor with16.9x30 tires, I only run about 10-12 PSI (depending on the weight of implement on the back) to get full tread contact.