In a large saucepan, combine the sugar, cornstarch and salt. Drain cherries, reserving juice; set cherries aside. Stir cherry juice into cornstarch mixture until smooth. Bring to a boil over medium heat, stirring constantly. Cook and stir until thickened, 1-2 minutes.
Remove from the heat; stir in the lemon juice and zest, extract and reserved cherries. Cool to room temperature. Serve with ice cream.