1. Peel a grapefruit, cutting away as much pith as possible. Over a bowl, cut flesh away from membranes and allow fruit to fall into bowl. Repeat with remaining grapefruit.
2. Halve avocados lengthwise and remove pits. Scoop out flesh with a spoon. With a stainless-steel knife, cut avocado lengthwise into 1/4-inch-thick slices. Sprinkle with 2 Tbsp. lime juice to keep from turning brown.
3. Whisk 2 Tbsp. lime juice with mustard, salt and pepper. Gradually whisk in oil.
4. Place lettuce leaves flat on a platter. Arrange grapefruit segments and avocado on top. Drizzle salad with dressing, sprinkle with chives and serve.