Train travel from Lucerne to Venice

Your best train connection (according to the present schedule) is by Euro Cities train, leaving Luzern at 7:47 am connecting in Milan to another Euro Cities train arriving Venice at 2:40 pm. This is the only itinerary with only one connection, other times also require a connection at Arth-Goldau. You can buy the tickets 3 months before your departure date at www.sbb.ch. There are Saver fares available for 75 chf per adult and 52 chf per child 6 to 16. If younger or older, different fares may apply. These are non refundable nonchangeable, much like airline tickets. The full fare for the family would be 392 chf.
No matter what, you will have to change trains in Milan. There also may be a less expensive ways by gettiing separate tickets to Milan, then to Venice from www.trenitalia.com. Milan's big draw is Leonardo Da Vinci's "Last Supper".

Thank you so much Sam. That info is exactly what I was looking for :)

Just to add to Sam's post - I usually try to make fewer connections while traveling because it's easier and less chance of anything going wrong (so I would probably book a train like he described - only changing in Milan), but wanted to note that Arth-Goldau is a very small station, would be quite easy to transfer through if you choose one of those schedules/routes instead. Like he said, book the Swiss part (to Milan) on sbb.ch and then the Italian part to Venice on trenitalia.com. If you can commit to a certain schedule, you can save a lot of money by booking ahead. I think crowds would probably depend more on the day of the week (weekday vs weekend). You'll have a seat reservation on the trains to Milan (not the Lucerne to Arth-Goldau if you choose to make that connection, but I wouldn't worry about it) and to Venice so even if it is a more crowded travel time, you'll be guaranteed a seat.