Mix sugar, milk, and lime juice together in a bowl. Mix in mashed strawberries.
Beat egg white in a glass, metal, or ceramic bowl until stiff peaks form. Fold into the strawberry-lime mixture. Pour mixture into a freezer-safe container. Cover with plastic wrap.
Freeze until almost firm, about 2 hours. Remove from freezer and stir thoroughly to break up chunks. Return to the freezer for 3 hours, stirring once every hour. Freeze until firm, 8 hours to overnight.
