Preheat a grill on medium heat. Grill the corn on all sides until nicely charred and tender. Once tender, lather with butter and lightly season with salt.
In a bowl, stir together mayonnaise, celery, lemon juice, and chives. Season with salt. Fold in chopped lobster meat.
Lay lettuce on a serving platter, then top with lobster salad. Garnish with avocado, more chives, and a squeeze of lemon.