Does it exist? If so, how many per day? What website to use for information about schedules? We are traveling in September. Thank you!
The schedules for September probably aren't up yet. You can use http://www.tgv-europe.com/ to check schedules from now to about 3 months ahead. If you eventually decide to buy from that website, enter Great Britain as your home country and as your ticket pickup location, otherwise you'll be kicked to the usually-more-expensive Rail Europe website. As you'll see, there are no nonstops from Milan to Lyon.
Tom is correct. It is too early for Fall schedules. Just use the same day of the week next week or next month for the schedules. The schedules change very little from quarter to quarter. Also bahn.de is a very easy site to use for schedule information for all European trains.
Web site policies about when routes are posted aside: there is no such thing as a high-speed train between these cities.
On the tgv-europe site it works to choose Great Britain as your ticket retrieval country if your route begins in France because then you can pick up your ticket at any SNCF station in France. If you were to book Milan-Lyon, you would need to have the ticket mailed to you at an address in Great Britain. The best site for detailed timetables for virtually all of Europe is the German Rail site. Your daytime routes are Milan-Geneva-Lyon and Milan-Chambery-Lyon. You can take a night train from Milan to Dijon and a regional train from there to Lyon.
I think tgv-europe.com gives you the option to print your tickets at home.
On tgv-europe-com some kinds of tickets can be printed at home but others cannot.