You would have to book tickets to see it first, and pick a time that fit with your train travel from Venice to Milano Centrale (2+hours). Then research luggage storage—-that isn’t easy as there is a lot of outdated information on the web. Apparently there is an on-site luggage deposit in the station, but off-site storage is cheaper. Also I have read of long lines to deposit and pick up luggage at the facility in the station, but that may be outdated. Here is the website for the on-site facility in case you are curious. Apparently the charge is €30 for 3 bags for 2-4 hours.
https://www.kibag.it/en/deposito-bagagli-milano/deposito-bagagli-milano-centrale/#pll_switcher
After stashing your luggage you need to make your way to the chapel by taxi or metro, in time for your timed entry. Then make your way back to the station in good time for your onward journey.
But you should ge more information, hopefully with first-hand experience, before deciding to do this. Just dealing with Milano Centrale—a large and noisy train station—-is enough for me.
Edit: I just re-read and see you might have 3 nights to spend between Venice and Paris. If the Last Supper is important, you could spend the first night in Milan and have the afternoon to spend there and see the Last Supper. I also recommend going up on the roof of the Duomo by stairs. It is amazing up there (we just did this at the end of August).
Book a hotel near the Milano Centrale station to save time getting back and forth from the station with your luggage. Hotel Berna comes highly recommended.
Then continue on to Luzern the next day and spend 2 nights there. That gives you time to explore the city and take a boat ride and mountain excursion if you like. Luzern to Paris is an easy trip with a single change at Basel if you choose the right train.