Preheat a well-oiled BBQ grill to medium-high, 300-400 degrees F.
Slice the avocados in half lengthwise and carefully remove the seed. Brush the exposed flesh with the honey-olive oil mixture, cover with plastic wrap and set aside in a cool place (do not refrigerate).
Chop the mangoes and strawberries and mix them with the vinegar, orange juice, and lemon juice. Let it rest at least 20 minutes so the ingredients can blend. Stir occasionally.
Spray your grill very heavily with PAM or another grilling spray.
Grill the avocados skin side down directly on the grill for 2 to 3 minutes, until the skin begins to lightly char and take on grill marks. Re-spray the grill and brush the flesh side of the avocados again with the honey-oil mixture and place the halves flesh side down on the hot grill for another 2-3 minutes.
With a spatula carefully remove the avocados from the grill and place them on a serving plate covered with a bed of lettuce, two halves per person. Fill the seed cavity with the mango-strawberry salsa, generously dribbling some on the top of each half. Serve with a spoon to scoop out the avocado flesh and salsa.
