Combine lemon juice, Dijon, 1/2 teaspoon salt, and 1/2 teaspoon pepper in a small bowl. Slowly whisk in olive oil until vinaigrette is emulsified.
Cut avocados in half, remove pits, and carefully peel off skin. Cut each half into 4 thick slices. Toss in vinaigrette to prevent them from turning brown.
Peel grapefruit skin and all the white pith with a large, sharp knife. Cut between membranes to release the grapefruit segments.
Arrange avocado slices evenly around the edge of a large platter, then arrange grapefruit segments in the center. Spoon vinaigrette over top, then sprinkle with more salt and pepper.