Purée lemongrass, cumin, shallots, garlic, ginger, sugar, salt, turmeric, cayenne, and water in a food processor, scraping down the side occasionally, until it's as smooth as possible, about 2 minutes. (Paste will not be completely smooth.)
Heat 3 tablespoons oil in a small pan over medium heat until hot but not smoking. Add lemongrass paste, then reduce heat to medium-low and cook, stirring occasionally, until paste begins to thicken and becomes fragrant, 8 to 12 minutes (I cooked mine for 10 mins). Transfer paste to a bowl and cool to room temperature, about 30 minutes.
While paste is cooling, trim fat off rack of lamb (or even better, have your butcher do it!) and pat dry. Place rack of lamb on a foil or parchment-lined baking sheet or in a pan. Then apply paste all over the top of the rack. Cover lamb with plastic wrap and refrigerate overnight - at least 12 and up to 24 hours.
Take lamb out of refrigerator 1/2 hour prior to cooking.
Preheat oven to 425 degrees on the Roast Setting. Use Bake, if your oven doesn't have Roast.
Cook lamb for 15 minutes undisturbed for medium-rare, internal temp of 125-130 degrees. (If your rack of lamb weighs more than 1 1/2 lbs, you will need to cook it longer).
While lamb is cooking, mix together lime zest and juice, remaining 1/4 cup oil, herbs, and salt and pepper to taste.
Remove lamb from the oven and let rest for 10-15 minutes before cutting into individual or double chops.
Place lamb chops on a platter and spoon herb salad over chops.