Place the strawberries, sugar, and water in a medium size saucepan over medium high heat and bring to a boil.
Lower heat a bit to medium-low and let simmer, stirring occasionally, until sugar dissolves and mixture thickens into a syrup, about 10 minutes.
Strain liquid into a heat-proof bowl or jar, pressing with the back of a wooden spoon to extract as much juice as possible. Discard solids (or save them for something amazing like ice cream toppings). Add lemon juice. Put in fridge to chill.
Place sprinkles on a small plate. Brush a little strawberry on rims of glasses and and place glasses upside down on plate to coat rims in sprinkles.
Pour milk into glasses and mix in 3-4 Tbsp strawberry syrup until combined. Taste and add more syrup if desired.