What train do I take to go from Venice to Lugano

It's up to you. There is one direct train (Venice dp 15.20) plus 14 trains with change at Milan. Journey time about 4 hrs.
Acquista il biglietto con le nostre offerte - Trenitalia https://www.italotreno.it/en www.sbb.ch/en https://www.seat61.com/

Rather than waiting for one daily direcdt train just take any train to Milan and then train to Lugano. Acquista il biglietto con le nostre offerte - Trenitalia yes for booking own tickets, at a discount if early enough to get those limited in number discounted tickets. In Switzerland if traveling to more than a few places check out Swiss Travel Pass and or Half-Fare Card or regional passes like Berner Oberland good in Lucerne and Interlaken areas - for lots on trains and passes check www.seat61.com; BETS-European Rail Experts and www.ricksteves.com.

As it's a long trip of 5 hours or so check firstclass fares too as sometimes they are not according to past posts not much more expensive than the cheapest 2nd class tickets remaining. Especially nice are the solo seats only found in first class - an aisle and window seat both - two can face each other with a table in between.

Thank you

What are your Swiss travel plans after Lugano - curious.