In a small saucepan, heat sugar and water over medium heat until sugar is dissolved, stirring frequently. Stir in lemon strips. Bring to a boil. Reduce heat; simmer, uncovered, for 5 minutes. Cool slightly.
Transfer to a pitcher. Stir in lemon juice; cover and refrigerate until chilled. Discard lemon strips. Stir in club soda. Serve over ice.