Combine 1 bottle club soda and water, stirring well.
Arrange lemon slices and cherries in a 6-cup ring mold; gently pour 1 cup club soda mixture into mold; freeze. Pour remaining club soda mixture over frozen mold; freeze until ready to use.
Combine lemon rind and juice, sugar, and 2 bottles club soda, stirring well. Let stand 1 hour, stirring frequently. Remove rind, and discard.
Unmold ice ring in a punch bowl. Gently pour lemon mixture, champagne, wine, and sherry over ring. Serve immediately.