In a medium saucepan, combine the cherries, sugar, and 2 tablespoons of water. Bring to a boil over medium heat.
Reduce the heat to low and simmer for 8-10 minutes, stirring occasionally, until the cherries have softened and released their juices.
Stir in the lemon juice.
If you prefer a thicker sauce, whisk together the cornstarch and 1 tablespoon of water in a small bowl until smooth. Pour this mixture into the simmering cherries and stir continuously until the sauce thickens, about 1-2 minutes.
Remove from heat and let it cool slightly before serving. The sauce will thicken more as it cools.
Notes
This cherry sauce can be stored in an airtight container in the refrigerator for up to a week.