1. Combine 1 1/2 cups water and sugar in a saucepan; bring to a boil, stirring until sugar dissolves. Remove pan from heat; add wasabi paste and lemon juice, stirring with a whisk. Cover and chill completely.
2. Stir in milk. Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon ice cream into a freezer-safe container; cover and freeze 1 hour or until firm. Drizzle each serving with honey.