In a medium saucepan, bring cherries, water, sugar to a boil on medium-high heat. Make sure to stir often so nothing sticks and burns.
In a small bowl, whisk the lemon juice and cornstarch until smooth.
Stir the cornstarch mixture into the cherries, and keep stirring.
If the mixture is too thick, add 1 tbsp of water.
Keep stirring, and keep cooking until the sauce reaches the desired thickness.
Remove from heat, let cool a bit, then taste. Add 1 tsp of sugar at a time, or 1/4 tsp lemon juice to taste, if needed.
Let cool completely before serving.