To prepare dressing, squeeze horned melon into a fine mesh strainer over a bowl; press with the back of a spoon to extract juice. Discard seeds. Add buttermilk and next 4 ingredients (through pepper) to bowl; stir with a whisk. Cover and chill.
Cook edamame according to package directions, omitting salt. Drain. Rinse with cold water; drain well.
Combine edamame, apple, onion, and lettuce in a large bowl; pour dressing over and toss gently to combine. Serve immediately.