Will pass work for Paris->Montreaux->Lucca->Rome?

Sure, the Global Pass is perfectly valid from/to those cities. The vast majority of European trains are included, notable exceptions :

- Ouigo low-cost high-speed trains in France (always regular high-speed trains on the same route)

- some mountain railways in Switzerland (often 25-50% discount)

- .italo high-speed trains in Italy, always in competition with Trenitalia (valid)

Have a look at the mandatory reservations on top of the pass in France and Italy (extra costs) : https://www.seat61.com/interrail-and-eurail-reservations.htm

There are ways to save money, for example by taking a regional train across the French-Swiss border.

Questions welcome. :)