What train is the quickest from Nice to Venice St Lucia station.
The best source for the answer to your question is the German Rail site which has detailed timetables for virtually all of Europe. Enter Nice Ville as your departure point and Venezia Santa Lucia as your arrival point. New timetables will go into effect on 13 June and Trenitalia (Italian Rail) hasn't uploaded theirs yet so the German Rail site is only complete through 12 June. After you get summary timetables for Nice Ville-Venezia Santa Lucia, click on the arrow to the left of each departure time to see the connecting points.
You'll find that you can leave as early as 05:23 and arrive in Venice at 14:10. Your fastest routes (7hr47min) mean leaving at 09:53 and arriving at 17:40 or leaving at 13:53 and arriving at 21:40.