parking in Venice

I was not aware that you could check luggage at the lot. The general recommendation is not to leave luggage in the car. But we have done it with no problems. Just don't make it obvious that luggage is there. I think on street parking with luggage is a greater risk but theft can happen to anyone at anytime.

There is luggage storage at Piazzale Roma.
http://www.trasbagagli.it/en/pg/view/53/luggage-storage-venice-piazzale-roma-airport

I've left a car parked at Tronchetto with a full trunk. Was a little nervous about it, but all was fine. We did back in the car all the way to the wall. The lot actually looked pretty good -- well lit and no obvious broken glass anywhere. I don't think there's anywhere to check luggage at the lot.

This this recent thread on the same question for more answers and an ability to store:

https://community.ricksteves.com/travel-forum/italy/parking-near-venice-ce827586-22e8-44e5-9f82-40225e2dfc6a

or https://community.ricksteves.com/travel-forum/italy/parking-near-venice

I parked at Tronchetto last July, and we left the luggage with them, they keep in the office where you pay for the parking. I don't recall the price, but it was reasonable. They were pretty responsive to e-mail, so I'd ask them.

I wouldn't leave the luggage in the car, the various levels are unattended, there wasn't a lot of foot traffic, and it's obvious anyone parked there in the afternoon or later is probably staying in town and not coming back until morning. While there wasn't a lot of broken glass around, that doesn't always mean the garage is safe, a skilled thief doesn't need brute force and broken windows to get into your car.

The lots have surveillance cameras. That of course doesn't guarantee 100% security.
You could use the baggage storage service in Piazzale Roma or with the lot, if they have it.