Prepare the grill for direct cooking over high heat (525° to 575°F).
Meanwhile, cut a slice about 1/3 inch off both ends of each lemon, then cut each lemon in half lengthwise. Lightly brush the cut sides of the lemon with 1 tablespoon of the oil.
Grill the lemons over direct high heat, with the lid closed, until nicely browned, 4 to 6 minutes, turning once. Remove the lemons from the grill and let cool. Set aside 2 lemons (4 halves) for garnish. Place a fine-mesh strainer over a small bowl and squeeze the juice from the remaining 4 lemon halves through the strainer. Discard the spent rinds and any seeds in the strainer. You should have about 1 tablespoon juice. Add the capers and the remaining 3 tablespoons oil to the lemon juice and whisk to form a dressing. Whisk in the chives, salt, and pepper, then taste and adjust the seasoning if needed.
In a small bowl mix together the rub ingredients.
Generously brush the halibut on both sides with oil and then season on both sides with the rub. Grill the halibut over direct high heat, with the lid closed, until the flesh is opaque in the center but still moist, 6 to 8 minutes, turning once. Remove the halibut from the grill.
Whisk the dressing one last time. Serve the fish warm with the dressing spooned over the top. Serve the reserved grilled lemon halves on the side.
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