1. Combine first 3 ingredients in a small saucepan. Bring to a boil. Stir in lavender. Remove from heat; cover and steep 30 minutes.
2. Pour lychee mixture through a sieve into a medium bowl. Discard solids. Stir in lemon rind and lemon juice. Place bowl in a large ice-filled bowl for 5 minutes or until cool, stirring occasionally.
3. Place 2 tablespoons water and cucumber in a blender; process until smooth. Stir into lychee mixture.
4. Pour mixture into an 8-inch square glass or ceramic baking dish. Cover and freeze until partially frozen (about 1 hour). Scrape with a fork, crushing any lumps. Freeze, scraping with a fork every 30 minutes, 1 1/2 hours, or until completely frozen.