Preheat oven to 375ᵒ. In a bowl, mix together the honey, Dijon mustard, thyme, lemon juice, salt and pepper. Set the bowl aside.
Salt and pepper the rack of lamb, and brush it with oil. Put is in a roasting pan and place in the preheated oven for 12 minutes. Turn and baste twice during this time. Add the onion, carrot, and garlic to the roasting pan, and roast for 10 more minutes. Once during the 10 minutes, turn and meat and stir the vegetables.
Remove the roasting pan from the oven and remove the lamb and place it in another oven proof pan.
Remove all the fat from the roasting pan. Add the wine to the vegetables and boil the liquid for a few minutes, and move the vegetables about with a spoon. When the liquid has been reduced by 1/2, strain it through a sieve into a small pan and keep warm. Press the vegetables through the sieve as well, but do not attempt to push all solids.
Meanwhile preheat the boiler at maximum heat. With the meat side of the rack up, brush the top rack with the reserved honey mixture
Put the meat under the broiler for 3 minutes, until the top of the rack is nicely caramelized.
Cut the rack into 8 chops, and arrange them in 2 plates with liquid of the roasting pan.