Lexus donut spare?

You need to check the tire size on your Lexus. The road wheels may be 17 or 18 inch, depending on whether you have a sport package, etc. The PiP uses a 15" road wheel, and the donut spare from 2010-2112 regular hatchback Prius will fit. They are available from auto dismantlers and others who deal in used parts, or probably at a dear cost from your Toyota dealer. Some posters here have found them online. See the thread "No Spare Tire" for more info. on the second page of this forum. The tire size you need is 135/80/16. It changed from the Gen II size, so make sure they give you the right one. There is a strap in one of the cargo underfloor compartments to use to tie it to the fixed rings in the cargo area to make it safe. Mine cost $160 delivered to the dismantler's yard, and had never been used.
Edit: I'm just making a guess, but the difference in size from 15" to 16" is because the spare tire itself is smaller than a regular tire. I apolgize for the error on the road wheel size.

 

I managed to find a seller on eBay who was selling an entire set of PiP tires and wheels, I bought it and am selling of 3 of the wheels/tires to local Boston PiP owners. The same seller has full sized wheel/tire combos from 2010/11 Priu, for about $200 shipped. The wheel design is a little different, but it will fit on the PiP.

Note: he seems to have sold the tire/wheel combo he had, he still has wheels for the 2012 Prius, you will need to get your own tire and get it mounted:

2012 TOYOTA PRIUS ALLOY RIM/WHEEL 15" | eBay

 

For sure, the answer is No. The IS250/350 use a 5x4.5 (or 5x114.3mm) bolt pattern. The Pip needs a 5x100 bolt pattern.