Combine white grapefruit, pink grapefruit, and orange sections in a large bowl.
Scoop out honeydew melon and cantaloupe flesh using a melon baller; add to the citrus in the bowl.
Toss avocado with 1 tablespoon lemon juice in a small bowl. Remove from the juice; add to the bowl of citrus and melons.
Whisk olive oil, 1/4 cup lemon juice, and balsamic vinegar together in a bowl. Stir in 1/3 cup chopped mint, honey, salt, and black pepper. Pour over citrus and melon mixture; toss gently to prevent mashing avocado. Garnish with fresh mint leaves.