Prepare a charcoal or gas grill for direct, medium-heat grilling. Cover a rimmed baking sheet with a piece of heavy-duty aluminum foil, then drizzle the foil with the canola oil and use a pastry brush to brush the oil all over the foil.
Place the fish skin-side down on the foil. Spread the mayonnaise over the flesh side of the fish, then sprinkle with the gin. Season generously with salt and pepper, then place the lemon slices evenly over the fish. There should be enough lemon slices to cover the fish. If not, slice another lemon.
Transfer the fish—with the foil still beneath it—to the grill grate. You may need help to do this; an extra set of hands helps complete this step with ease. With a pair of tongs, curl the edges of the foil around the fish, but do not completely enclose the fish in the foil.
Cover the grill (if using charcoal, open the vents) and cook until the fish flakes easily when the tip of a paring knife is inserted into the fleshy side, 10 to 12 minutes. Carefully transfer the fish (still on its sheet of foil) back onto the rimmed baking sheet.
Let the fish cool for a minute, then use a spatula to transfer it to a platter. Remove and discard the lemon slices, garnish with the fresh dill, and serve immediately.