Finely grate beet on small holes of a box grater directly onto a piece of cheesecloth. Gather up sides of cheesecloth to make a bundle and squeeze beet tightly over a small bowl to extract as much juice as you can. Transfer 2 Tbsp. beet juice to a small bowl and set aside.
Bring sugar, sumac, and 1 cup water to a boil in a small saucepan. Reduce heat and simmer, stirring, until sugar dissolves, about 5 minutes. Let sumac syrup cool.
Strain sumac syrup, lemon juice, and reserved beet juice through a fine-mesh sieve into a measuring glass and give it a good stir.
Divide beet-sumac syrup among 4 ice-filled glasses, then top with club soda.
Do Ahead: Syrup can be made 1 week ahead. Cover and chill.
