When I look at your route on your other thread, the first destination where you might need a car is Colmar, France. When you say "lease a car", is it a standard car rental, or is it one of the leasing programs of some European automakers? If it is just a standard car rental, you might save a lot of money starting the rental in Colmar!
Now, back to your question.
I would take the A10 past Genoa to the A26 due north, and cross into Switzerland via Simplon pass (no issue in May,) typically kept open year-round). Then drive to Goppenstein for the Lötschberg car-train shuttle. The other side, Kandersteg, is not far from Interlaken.
The other main option, without a train shuttle, would be to go via Milan, Lugano and the Gotthard tunnel, but Nufenen pass might not be open yet in which case you would have to drive all the way north to Stans, then south over Brünig pass.
Third option, valid if Nufenen pass is closed, is via Aosta, the Great St Bernard tunnel, and Bern.
Either option is a very long day.
You need to purchase a toll sticker (vignette) at the border to drive on Swiss motorways. The motorways are realistically unavoidable.