Thinking about this itinerary for 11-12 days in July. I will be traveling with my husband and two teenaged children- girl, 16, boy, 14.

• Fly into Zurich, go directly to Lucerne for 3 nights- is 3 nights too much?
• From Lucerne, take the train to Lake Como for 4 nights. Thinking about staying in Varenna in an apt/airbnb as there seems to be limited options for a quad hotel room -Take the train to Venice for 4 nights and fly home from here.

Any thoughts on the itinerary, particularly how much time we are spending in each spot? Any advice would be great appreciated!

It depends on what YOU want to see and experience ... but 3 nights is only 2 days, and I found MORE than enough to do in / around Lucerne for that amount of time.

A good guidebook should help you plan.

It's feasible. Locistically, it might be easier to stay at Lugano instead of Varenna.
Trains:
Zurich airport - Lucerne, 1 1/4 hrs, journey; trains about every 30 min
Lucerne - Lugano: 1 3/4 hrs journey; trais about every 30 min
Lugano -`Venice: 4 1/4 hrs journey. Direct train Lugano dp 10.30, otherwise change at Milan (every hr).

In the improbable case you would like to see the Swiss Alps, you could reach Lugano from Lucerne over the Alps:
Lucerne - Brunig Pass - Grimsel Pass - Nufenen Pass - Gotthard Pass - Andermatt - Goeschenen - treno Gottardo - Bellinzona - Lugano.
That would take a whole day.

Four nights in Venice is nice for a relaxed visit, but you might be underestimating how warm and crowded Venice can be in July. I’m also planning something similar while checking options for a Schengen trip.

Check the flight times from Venice to home. Also connections depending on where you live. Departures can be painfully early. Connections can complicate. I'm West Coast U.S., and it's always easier to fly in to Venice rather than out of Venice.