Heat oil in a medium skillet over medium-high. Season lamb with salt and pepper and arrange in pan in a patty about ¼” thick. Cook, pressing occasionally to help meat make contact with pan, until underside is browned and very crisp, about 5 minutes. Carefully turn, pouring off excess fat (reserve 2 Tbsp), and cook until other side is crisp, about 5 minutes.
Break up lamb into small pieces. Mix in garlic, red pepper flakes, and cumin. Cook, stirring occasionally, until spices are fragrant and lamb is cooked through but still juicy, about 2 minutes. Transfer lamb mixture to a bowl with a slotted spoon.
Place lentils and 2 Tbsp of reserved fat in same skillet, season with salt and pepper, and cook, tossing occasionally, until lentils start to brown and crisp, 5–8 minutes. Return lamb to skillet and toss to combine and warm through. Remove from heat and stir in cucumber, cilantro, and parsley.
Spoon yogurt onto plates and top with lamb mixture, then some more cilantro and parsley. Serve with flatbread and lemon wedges.