Cut peel and white membrane from grapefruit. Working over a strainer set over a bowl, cut between inner membranes and fruit to release segments into strainer. Squeeze juice from membranes into bowl (discard membranes); you need about 1/4 cup juice (reserve any remainder for other uses).
Add lemon juice, mint, shallot, and honey to grapefruit juice, and mix.
Peel and pit avocados; cut lengthwise into 1/2-inch-thick slices. Set a frise leaf on each of 4 salad or dinner plates and arrange equal portions of grapefruit segments and avocado slices on top.