Russell,
As Larry mentioned, that's a very easy trip. The first leg from Lucerne to Milan will take about four hours, depending on which departure you choose. The next leg from Milan to the Cinque Terre will depend to some extent on which of the five Cinque Terre towns you'll be travelling to. Which of the five towns are you planning to stay in?
You can research the rail trips using either the Bahn.de (German Rail) or the SBB.ch (Swiss Rail) websites. You can also research trips within Italy using the Trenitalia (Italian Rail) website.
As mentioned previously, it's far too early to be researching trips for November 2014. As I recall, the schedules for the latter part of the year will be updated on the website in June. However, you can get a good idea by checking the same time and day of the week that you'll be travelling, as it's not likely the schedules will change much. I'd suggest looking about three months from your travel date.
You may be able to purchase tickets for the entire journey on the Swiss Rail website. If not you can purchase tickets for the Lucerne-Milan segment on the Swiss rail site and the tickets for the Milan-Cinque Terre segment on the Italian rail site. One point to mention is that if the Italian segment involves Regionale trains, it's best to just purchase those tickets when in Italy. There are a few potentially expensive "caveats" regarding rail travel in Italy. If you need further information on that, post another note.
Happy travels!