Which Gulf lake saw a British victory over U.S. gunboats before New Orleans?

The Gulf lake where Britain defeated U.S. gunboats before the Battle of New Orleans was Lake Borgne.

The Battle of Lake Borgne took place on December 14, 1814, as British forces prepared to invade New Orleans. U.S. naval commander Thomas ap Catesby Jones stationed five gunboats, along with the tender USS Alligator and schooner USS Sea Horse, in the shallow waters leading toward Lake Pontchartrain and the city.

Because the water was too shallow for the main British warships, Commander Nicholas Lockyer led about 980 sailors and Royal Marines in a flotilla of roughly 40 armed boats. After rowing for many hours, the British attacked and boarded the American vessels. They captured all five gunboats and removed a key American screen protecting the approaches to New Orleans.

Lake Pontchartrain was nearby and formed part of the wider approach to New Orleans, which makes it a plausible distractor, but the battle itself occurred on Lake Borgne. The British victory allowed their army to land nearby and contributed to the panic and uncertainty preceding the January 1815 battle.