Make lemon ice ring, if desired: Arrange 16 to 18 lemon rounds (about 2 lemons) in the bottom of an 8-inch tube or bundt pan, overlapping the slices. Add ice cubes (this will help keep fruit from floating to the top as the water freezes) and fill the pan with 3 to 6 cups water, enough to cover the lemons. Freeze until solid.
Combine the gin, Suze, and vermouth in a large pitcher or punch bowl. Cover and chill for at least 2 hours or overnight. If using, remove the ice ring from the pan and float in the punch. To serve, ladle into ice-filled glasses.