From my own experience, just lowering the car with stock wheels and tires won't cause a clearance issue.
Without considering, (understanding) backspacing, I bought a set of 195/55-15 BFG Sport Comp 2 tires (approximately the same diameter as the stock 13" tires) and four 10-hole fox body Mustang wheels which have 5" backspacing. When the wheels and tires were installed and the car, a '75 Runabout, was lowered, the upper a-frames dug into the front wheels and locked the car down solid. The back tires cleared the inboard wheel well structure by approximately a half inch. There was a lot of outer tire clearance front and rear.
I ended up having to trim the upper A-frames fore and aft of the ball joints and add a small wheel spacer (1/4" or 5/16", I can't remember now) to clear the 10-hole fox body wheels of the upper A-frames.
Knowing what I now know, I'd definitely double check backspacing if I planned to go with wider wheels and tires.