Venice isn't in a lake, it's in a lagoon, a salt-water arm of the Adriatic sea.
The Venetian Lagoon (Italian: Laguna di Venezia; Venetian: Łaguna de Venesia) is an enclosed bay of the Adriatic Sea, in northern Italy, in which the city of Venice is situated. Its name in the Italian and Venetian languages, Laguna Veneta—cognate of Latin lacus, "lake"—has provided the English name for an enclosed, shallow embayment of salt water, a lagoon.
The lagoon is OPEN TO THE SEA.
Rainfall has NO EFFECT on the water levels in Venice (unless it's so severe that it changes the levels of the sea) because if the lagoon is low, the sea rushes in to fill it back up. And if the lagoon is over-full, it rushes out into the ocean.
This is nothing more that an unusually low tide (which is that you'd be told if you were sourcing a legitimate news source).