Wash strawberries well. Remove stems, hull, and cut into quarters
Place strawberries, sugar, ¼ cup water, and lemon juice in a large saucepan and heat over medium-high heat
When the mixture comes to a light boil, reduce heat and simmer 8-10 minutes or until strawberries become soft and syrup thickens.
Pour mixture into liquid measuring cup or jar through a fine mesh strainer (this will help remove the seeds). Press the strawberries gently to release excess juices. Skim foam from the syrup if needed. Allow to cool before serving.
If syrup is too thin, return to sauce pan and bring to a simmer. You want the syrup to be thick enough to coat a spoon. Thicken by combining ¼ cup water and 2 tablespoons cornstarch. Add slowly, stirring constantly, until desired thickness is reached.
Allow to cool. Stir in 2-3 tablespoons of syrup to 2 cups of milk.
Stir until pink and well combined. Store excess syrup in an airtight container in the refrigerator for up to 5 days.