Prep. Slice the avocados in half lengthwise and carefully remove the seeds. In a small bowl, mix together the honey and olive oil. Brush the exposed flesh with the honey-olive oil mixture, cover with plastic wrap and set aside in a cool place (do not refrigerate).
Peeled and pit the mango then cut into 1/2-inch (1.3 cm) cubes. Remove stems from the strawberries then cut into 1/2-inch (1.3 cm) pieces.
In a medium bowl, combine the mango, strawberries, vinegar, orange juice, and lemon juice. Let sit for at least 20 minutes, stirring occasionally, so the flavors can blend.
Fire up. Preheat the grill to 325°F (163°C).
Cook. Grill the avocados, skin side down, for 2 to 3 minutes, or until the skin begins to lightly char and take on grill marks. Oil the grill grates, brush the flesh side of the avocados again with the honey-oil mixture and place them flesh side down on the grill for 2 to 3 minutes.
Serve. With a spatula, carefully remove the avocados from the grill and place them on beds of lettuce on warm serving plates, 2 halves per person. Fill the seed cavity of each avocado half with the mango-strawberry salsa. Serve with spoons to scoop out the avocado flesh and salsa.
