Toast the cumin and coriander seeds in an 8-inch skillet over medium-low heat, shaking the pan occasionally, until fragrant, 1 to 2 minutes. Transfer to a mortar (or a mini food processor or spice grinder). Add the lemon zest, 1-1/2 tsp. salt, and 1/2 tsp. pepper and finely grind. Rub the spices all over the lamb chops; let sit at room temperature for 30 minutes.
Meanwhile, put the chickpeas, reserved cooking liquid, and 1-1/4 cups water in a 4-quart saucepan over medium-high heat and simmer for 5 minutes. Reserve 1/2 cup of the liquid, drain the chickpeas, and transfer to a food processor. Add 1/2 tsp. salt and a few grinds of pepper and pulse until the chickpeas are coarsely chopped. With the motor running, slowly add the reserved 1/2 cup liquid, the crème fraîche, 1/4 cup of the oil, and 1 tsp. of the lemon juice; purée until smooth. Season to taste with salt and pepper; keep warm.
Heat 2 Tbs. of the remaining oil in a 12-inch skillet over medium-high heat. Working in batches, cook the lamb chops, undisturbed, until deep golden-brown, 3 to 5 minutes. Flip and cook until medium rare (130°F), 4 to 6 minutes, adding more oil as needed for the second batch. Transfer to a plate to rest. Wipe the oil from the skillet, removing any burnt bits but leaving the caramelized morsels behind.
Add the remaining 1/4 cup lemon juice and 2 Tbs. water to the skillet and bring to a simmer over medium heat. Add the butter, a few pieces at a time, whisking until incorporated. Remove from the heat and season to taste with salt.
Divide the chickpea purée among 4 dinner plates and top with 2 lamb chops each. Drizzle with the pan sauce, sprinkle with the mint, and serve.