Bring water, mint, and sugar to a boil in a 1- to 2-quart saucepan, stirring until sugar is dissolved, then reduce heat and simmer, uncovered, 3 minutes.
Add lemon juice and pour through a fine-mesh sieve, pressing hard on solids and discarding them, then cool.
Freeze mixture in a 1 1/2- to 2-quart shallow nonreactive metal container, stirring and crushing lumps with a fork every 30 minutes, until evenly frozen, 2 to 3 hours. Scrape with a fork to lighten texture, crushing any lumps. Spoon into glasses or bowls.
