Combine first 5 ingredients in a large bowl, stirring until sugar dissolves. Add milk and whipping cream, stirring until well blended.
Pour cream mixture into freezer container of a 2-quart ice-cream maker, and freeze according to manufacturer's instructions. (Freezing instructions will vary among manufacturers.) Pack freezer with additional ice and rock salt, and let stand 1 hour before serving. Serve with Lemon Crunch Lace Cookies. Garnish, if desired.