The duo showed up to Giorgio Baldi Italian restaurant in black leather biker jackets and helmets.
Gaga, 30, wore faded ripped jeans and spiked black boots, while Cooper, 41, opted for navy pants and grey sneakers as he drove the Ducati bike, reported Us magazine.
Fans previously saw Gaga, who is engaged to longtime partner Taylor Kinney, atop a motorcycle on her 2011 Born This Way album cover.
The "American Sniper" actor is currently dating Irina Shayk. The pair, who started dating in April 2015, made their red carpet debut during Paris Fashion Week on March 8.