Preheat the oven to 400 degrees F (200 degrees C).
Heat a dry saucepan over medium-high heat. Add coriander, caraway, and cumin seeds; toast until smoky, about 2 minutes. Transfer to a mortar and pestle and roughly grind the spices together.
Rub spices over both sides of the lamb; pat down to make a crust. Season with salt and pepper.
Heat 1 tablespoon olive oil in an oven-proof skillet over medium-high heat. Add lamb, fat-side down. Cook, flipping halfway, until both sides are browned, about 5 minutes. Immediately transfer the skillet to the oven.
Roast lamb in the preheated oven until no longer red in the center, about 8 minutes. An instant-read thermometer inserted into the center should read at least 130 degrees F (54 degrees C). Remove from oven and let rest, about 5 minutes.
Combine mint, cilantro, lime juice, agave nectar, vinegar, and garlic in a food processor. Season with salt and pepper. Process until finely chopped. Slowly drizzle in 1/2 cup olive oil while blending to make the sauce.
Slice the rack of lamb. Spoon the mint and coriander sauce over each serving.
