Hull and halve the strawberries. Place them in a bowl, sprinkle over the sugar, mash lightly with a fork, and toss to combine. Let sit for 10 minutes (this is called macerating) until some of the juices release. Use a slotted spoon and transfer the berries into a small pot, leaving most of the juices in the bowl. Whisk the cornstarch and lemon juice into the juices until dissolved.
Place the pot over medium heat, and add the lemon zest. Stir in the lemon juice and cornstarch mixture. Heat, stirring frequently, breaking up the berries as you stir, until bubbly and thick, about 5 minutes. If you want a smother sauce you can transfer the mixture to a food processor and pulse or puree. Let cool to room temperature.