Pour lemon juice into a small mixing bowl and slowly add olive oil in steady stream, while whisking to emulsify. Whisk in dijon mustard, salt, and pepper. Set aside.
Peel and segment grapefruit with a sharp knife, ensuring all white pith is removed. Place segments in a medium mixing bowl. Thinly slice fennel and add to the grapefruit. Slice or dice avocado and add to the mixture.
Drizzle vinaigrette over salad and lightly toss to combine. Season with additional salt and dried basil (if using). Serve immediately.
Recipe by Megan Peck Cooks at http://meganpeckcooks.com/2015/01/avocado-grapefruit-fennel-salad/