I've got 315/35R17 Goodyear Eagle F1s on my '95. They are the absolute maximum.
I don't have any issues with rubbing the fender lip but my car is only lowered about 3/4". If its lowered more than that it will def. be a problem.
They will likely rub the exhaust if you've got 2.5" or larger. My car dumps out of the mufflers so no issues there.