1. Whisk together first 6 ingredients in a small bowl. Combine grapefruit and next 3 ingredients in a medium bowl. Drizzle with 2 Tbsp. vinaigrette, tossing to coat.
2. Place lettuce on serving plates or a platter. Cut avocados in half; remove and discard seeds. Carefully remove avocado halves from peels, discarding peels. Rub 2 Tbsp. vinaigrette over avocado halves. Top lettuce with avocados, and spoon grapefruit mixture over avocados. Serve with remaining vinaigrette.