Combine the yogurt, 1 tablespoon lemon juice, 1/4 teaspoon each lemon zest, dried mint and salt, and a few grinds of pepper in a small bowl. Set aside.
Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the shallot and cook, stirring, until tender, about 4 minutes. Add the lentils and cook until warmed through, about 1 minute. Transfer to a large bowl and toss with the remaining lemon zest and juice, the cherry tomatoes, cucumbers, parsley, pita chips, 2 tablespoons olive oil, 1/2 teaspoon salt and a few grinds of pepper.
Wipe out the skillet and return to high heat. Season the lamb chops with salt and pepper and rub all over with the remaining 1 tablespoon olive oil and 1 teaspoon dried mint. Add 2 chops to the skillet and cook, turning once, until well browned, 4 to 7 minutes. Transfer to a plate and tent with foil to keep warm. Repeat with the remaining 2 chops.
Divide the lamb chops among plates. Serve with the lentil salad and yogurt sauce.