Chop lobster meat into 1/2-inch pieces, then place in a large mixing bowl.
Remove skin and pit from avocado, then cut into 1/2-inch pieces and add to the bowl.
Slice cherry tomatoes in half and thinly slice the scallions. Add the tomatoes and scallions to the bowl, then place the bowl in the refrigerator while you make the basil mayonnaise.
Add basil mayonnaise to the bowl of lobster mix. Gently fold together (so as not to break up the avocados—you want to leave them as whole as possible). Place the remaining mayonnaise back into the refrigerator.
In a large sauté pan or griddle, use the butter to cook the rolls on each side until golden brown. Remove from heat and spoon in the lobster salad. Garnish with chopped fresh basil if desired.