Mary, There is no need to go anywhere first to catch a train to somewhere. Trains are an interconnecting network. There are 1838 stations in Switzerland, and you can travel by train from any one of those (including Luzern) to any other one, or to most other places in Europe (including Milan).
Go to the SBB (Swiss Federal Railways) website: https://www.sbb.ch/en/
Enter from: Luzern, to: Milano Centrale, and your desired date and time and click on [Search].
And it will show you all the options. There is roughly 1 train per hour, and it takes 3½ hours.
The SBB website always find the quickest route, which is in this case the main line to Italy through the Gotthard tunnel under the Alps. The longest rail tunnel in the world.
The Bernina route is an alternative route that goes over the Alps, and is very scenic. It is however in the eastern side of Switzerland, a long way from Luzern. If you want to go that way, add "via Chur Tirano" to your search and that will force the routing. This will take a lot longer (10 hours+). I would not try to do that in one day. If you want to go that way include an overnight stop.