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To Make the Lamb:
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Heat the Oven: Position a rack near the center of the oven and heat to 350 degrees (325 degrees convection).
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Trim the Lamb: If there is more than a thin layer of fat left on the racks, trim them so that only a thin layer remains.
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Do not attempt to remove all the fat, and be careful not to cut away any of the precious meat.
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Sear the Racks: Pat the lamb dry and season the meat all over with salt and pepper.
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Heat a heavy skillet (12-inch cast iron works well) over high heat.
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Lower one rack, meat side down, into the hot skillet.
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If theres room without crowding, sear the other rack at the same time.
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Its okay if the bone ends extend over the side of the skillet (your objective here is to get a good sear on the meat; the bones dont need to brown).
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When the top is nicely browned, 2 to 3 minutes, turn with tongs and brown the bottom for 2 to 3 minutes.
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Remove and repeat with the second rack, if necessary.
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This can be done, up to 2 hours ahead.
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Leave the meat at room temperature.
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(If you wish to protect the tips of the rib bones from possibly charring, cover them with a thin strip of aluminum foil.
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I dont bother as it doesnt affect the flavor, and I like the appearance of a little char.)
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Roast: Transfer the racks, bone side down, to a heavy-duty rimmed baking sheet or shallow roasting pan.
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You may need to interlock the bone ends to make the racks fit.
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If possible, arrange the racks so the meaty part faces the outside of the pan; this will help them to cook more evenly.
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Roast until an instant-read thermometer inserted in the center of the meat reads 125 to 130 degrees for rare to medium-rare, 20 to 25 minutes, or 135 to 140 degrees for medium-rare to medium, 25 to 30 minutes.
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Rest, Carve, and Serve: Transfer the lamb to a carving board, preferably one with a trough, to rest for 5 to 10 minutes.
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Carve by slicing down between the rib bones, cutting into single rib chops (1 bone each) or double rib chops (2 bones each) as desired.
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Serve, spooning any carving juices over the top.
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To Make the Relish:
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In a small bowl, combine the figs, mint, pine nuts, garlic, and lemon zest.
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Stir to combine.
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Drizzle in the oil and lemon juice.
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Season with salt and pepper to taste.
