Assuming you want to pick up the car immediately after landing at LIN, I would go to the San Donato Metro station which is very close to the freeway and only 10 min from Linate.
Then from the San Donato subway station you can take the M3 (Orange) Comasina direction, change at DUOMO and take the M1 (Red line) toward Rho or Bisceglie, get off after a couple of stops at Cadorna or Conciliazione, then walk. If all planets align (i.e. subway train departs exactly when you get to the station), from San Donato to Conciliazione you can make it in 30 min. Add the time of driving there, getting lost a bit, parking and taking the train, and you can be at the Last Supper in about 1.5hr from the moment you pick up the car at the airport.
The problem is...
Assuming the plane lands on time, you'll need an hour to deplane, baggage claim, rental car paperwork and pick up.
So in the best of circumstances you can be at the Last Supper no sooner than 1:30-2pm.
Assuming more planets align and you have the ticket entry for that time, you need 30 min. to visit the place. So maybe you are done by 3 or 3:30pm (more planets have aligned). You are now ready to return to San Donato to the car.
You made it back to San Donato and it's now past 4:00pm, maybe close to 5pm. Pick up your car in one of the multistory parking structures at San Donato (hopefully the car wasn't burglarized or the catalytic converter stolen, more planets to align), and you are ready to drive to Tuscany. Fortunately San Donato subway station is right next to the A1 freeway entrance so less chance to get lost in city traffic.
In a previous post you mentioned your villa is near Cerbaia. I can assure you that 3 hours aren't enough to drive from Milan to Cerbaia. Let's make it 3.5 hours plus pit stops (I presume you'll need a bio pit stop along the way, if not something to eat). So you are looking at an ETA at your villa maybe by 9pm (if all planets have aligned).
It has been a long journey and a long day. Time now to rest and look at the planets in the sky, which by now should be all aligned for you to view in the beautiful Tuscan sky.