score:5
If you want to travel by train from Lyon to Milano, it is not necessary to pass through Geneva or any other part of Switzerland. The most straightforward option is to take a regional train (TER) from Lyon's Part-Dieu station to ChambΓ©ry and then a TGV to Milano. This train is going to Milano via the Maurienne valley and Torino. At the moment there are two or three TGV trains per day linking Paris to Milano via ChambΓ©ry and Torino.
The TGV 9249 seems to fit your needs, as it does not cross Switzerland. On the 12th of May, you can leave Lyon Part-Dieu at 14h40 by the regional train bound to Bourg-Saint-Maurice. Ar 16h00 you will arrive at ChambΓ©ry-Challes-les-Eaux, where you will have to get out and wait for the TGV 9249 to Milano, leaving from there at 17h43.