Add lemon juice, salt, and tarragon to the reserved grapefruit juice; season with cracked black pepper. Whisk in extra virgin olive oil in a slow, steady stream. Add grapefruit sections and toss gently.
Brush 2 teaspoons lime juice over flesh of avocados.
Place each avocado half on a plate. Top with grapefruit mixture, dividing evenly. Serve immediately.