Well stock tire size is pretty much 25". Going to a 30-32" tire means that you are going to have a tire that is 2.5-3.5" taller and wider in the wheel well. I'm pretty sure there's no room in the wheel well for a tire 3.5" bigger on each side of the wheel well. That means that you have to lift as you suggested.
I've been looking into getting a Suzuki Sidekick as a beater vehicle. It is IFS (independent front suspension) like the PT. Most lifts for it locate the front diff lower than stock. Why? Because lifting the vehicle causes the cv joints on the axles to run at angles greater than they were designed for. I would think you likely couldn't lift more than 2" without running into issues with cv bind. At that point you are looking at either running lowering the engine/tranny to accommodate, or you're looking at having customized axles built which isn't cheap. You still may run into the issue that with the full amount of travel you run into rubbing on either the top or sides of the fender. Also expect problems when turning the wheel full lock with rubbing on the insides of the fender lining.
I would think to do it right fitting a 32" tire with a 4" lift, you'll be looking at spending a small fortune and you'll still have a vehicle that has the off road ability of a crotch rocket.
What I would suggest if you are very seriously wanting to go for this look AND want a functional rig is this: Start looking at listings for wrecked Jeep Wranglers with the 3.8L engine. The old Jeeps use an inline 6 which is far too long for the PT engine bay, the 3.8 is more compact. Buy a wrecked Jeep, chop the frame to fit the PT. Drop the PT onto the Jeep frame. You end up with a true 4x4, anything aftermarket for the drivetrain/suspension you want, and a unique looking rig. It just wouldn't be cheap.
This is the only 4x4 I've ever come across. Unfortunately they had to extend the front end, the wheelbase is wrong, the engine bay just looks weird the way they've blocked it off. If they'd worked with smaller components it would have looked better, but hey, I'd still drive that!
Ben
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2001 Red PT Cruiser Limited, 16" OEM alloys, Airaid CAI, Screamin' Demon coil and Livewires, some shiny stuff inside, Alpine deck, Alpine four channel amp, Alpine PLT5 sub, Hertz speakers in 4 corners, Keystone ram air hood, 6000k 55w HID high beams, 6000k 35w HID fog lights, new stone chips every day to add character.
2007 Suzuki King Quad 700 4x4 for when the road gets bumpy.