Line a large rimmed baking sheet with parchment paper. Arrange cucumber slices in single layer on prepared sheet. Freeze until solid, about 1 hour. DO AHEAD Can be made 2 days ahead. Cover and keep frozen.
Combine gin, liqueur, lemon juice, salt, and 2 cups ice in a large pitcher. Cover and refrigerate until chilled, about 2 hours. Stir club soda and frozen cucumber slices into pitcher. Fill 12-ounce highball glasses with ice. Pour cocktail into glasses and serve.