Step 1

In a saucepan, combine the lemon quarters with 1 cup of water and the salt and cook over moderately low heat until the lemon peels are tender and the liquid is reduced by half, about 30 minutes. Let the lemons cool in the brine.

Step 2

Transfer the lemons to a work surface; finely chop. Return the chopped lemons to the brine and refrigerate until chilled.

Step 3

Set up a grill for indirect cooking by lighting only one side of a gas grill or raking hot coals to one side of a charcoal grill. In a bowl, whisk together all of the spices. Brush the lamb ribs with lemon juice; season all over with the rub.

Step 4

Arrange the ribs on the grill. Cover and cook for about 1 hour, until well browned, maintaining a temperature of about 300°; add more coals if needed.

Step 5

Layer 2 large sheets of heavy-duty foil on a work surface and set 1 rack of ribs, meat side up, in the center. Fold the foil tightly around the ribs. Repeat with the second rack of ribs. Arrange the rib packets meat side up on the grill. Cover and grill for 1 hour, until tender but not falling apart, turning the packets over after 30 minutes. Transfer to a baking sheet and let rest for 15 minutes, then unwrap.

Step 6

Set the grill up for direct cooking by lighting all of the burners or raking the hot coals. Grill the rib racks meat side down over moderately high heat, turning once, until lightly charred all over, about 6 minutes total. Transfer to a carving board, tent with foil and let rest for 10 minutes. Cut the ribs between the bones; serve with the preserved lemons.