In a small saucepan over medium-low heat, bring sugar, 1/2 cup water, and the apricots to a simmer. Cover and cook until apricots are completely tender, about 4 minutes.
Carefully transfer apricot mixture and lemon juice to a food processor and pulse until sauce is blended but still slightly chunky. Taste and add more sugar if you like. Transfer to a serving bowl. Serve warm or chilled.
Make ahead: Up to 1 week; keep chilled.
Note: Nutritional analysis is per 2-tbsp. serving.