In a saucepan off the heat, combine the sugar and cornstarch. Add the cherries and lemon juice. Mix thoroughly. Place on the heat and bring to a boil. Cook for 5 minutes or until the cherries are tender and the syrup thickens.
Pour into a bowl and cover with plastic wrap directly on the surface of the sauce. Let cool. Refrigerate for 2 hours or until completely chilled.
The compote keeps up to 2 weeks in the refrigerator, or freeze.