Are all the passes shut all year? No. France, Italy and Switzerland are not all cut off from each other for road traffic for months on end.
Will all passes be open to you in late May? Probably not, especially the non-motorway very high passes.
Will you be able to get from Lyon to (possibly) Turin in late May on a motorbike? Yes, unless there is some kind of natural catastrophe which embraces Europe. If it gives you comfort, we went Calais > Milan > Ancona at Easter for the Turkey Trot and Calais to Algeciras another Easter, for the Moroccan Dash, all on motorbikes. Easter is always well before late May. Both routes cross mountains, we simply took the roads / tunnels that were open to us; if we had listened to the “All the routes / passes will be shut” cries, we’d never have left home. You can do the same, I’m sure.
Will anyone give you all the alternative routes and hotels for your trip from Lyon to (possibly) Turin in late May? Probably not, as posts #2 and #3 suggest, there are too many variables. Likewise your Italy / Switzerland / France leg. Just look at a map and the weather forecast when you are sat in Lyon in late May and work out how to get to Turin (assuming you do still want to go there then) using a map. Google will even route you away from roads that are shut. Do the same, sat on the Italian lakes, to get to Belfort in France.