In a small heatproof bowl, combine the sugar and boiling water, stirring until fully dissolved. Pour the lemon juice into a blender. Add the frozen strawberries, cold water, and sugar mixture. Blend on high speed until the strawberries are fully crushed and the juice is completely smooth.

Taste and adjust sweetness if needed. Pour into a tall 15-ounce/450-milliliter glass and serve immediately while cold.