For the marinade, I recommend minced garlic, mint leaves, rosemary, thyme, salt & pepper, 1 Tbs of honey, olive oil, and balsamic or apple cider vinegar. Amounts will depend on how many racks you're doing, but if it is just one (we get ours at Costco and it is about 8 ribs), you want about 1/4 to 1/2 cup of the vinegar and a tablespoon or so of the mint leaves and minced garlic each.
Put it all in a ziploc bag with your rack of lamb—be sure the rack (meat portion) is covered completely with the marinade—and refrigerate overnight at least. Take it out and bring to room temp an hour or so before putting it on the grill. I like the flavor of mesquite, so I'll put a wet chunk on the grill to smoke through this whole process. I start with a very high heat, searing the top/meat-side first to get some nice grill lines—maybe 5 to 10 minutes. Then I turn off or turn all the way down the center burner, leaving the meat over the center burner.
Let it finish over indirect heat until the internal temp is about 120; we like rare to medium rare. Go to 130 if you like more medium rare. Go to 140 if you want to ruin your expensive rack of lamb. Go to 150 if you really don't care about flavor and you're okay with chewy. When you reach your desired temp, remove the rack and leave it on your cutting board for at least 5 minutes to calm down and let the juices settle. Of course, if you let it go to 150 there won’t be any juices left and you might as well use the 5 minutes to go out to the garage and grab a saw or throw it in the trash. This wonderful meat goes nicely with a creamy risotto and pares with either a Cabernet or pinot noir. Bon Appetit'!