Combine orange juice, lemon juice, and sugar in a pitcher; stir until the sugar is dissolved. Cover pitcher with plastic wrap. Chill in refrigerator 15 minutes. Add the lemon-lime soda and the bourbon liqueur. Serve over ice.
Refrigerate until chilled, about 15 minutes. Gently stir lemon-lime soda and bourbon liqueur into the orange juice mixture. Pour into cups filled with ice to serve.