Set oven racks in top and middle positions and preheat oven to 450°F. Mix lemon juice, yogurt, ginger, garlic, 1/2 tsp. salt, cumin, coriander, cayenne and turmeric in a blender until smooth.
Place pork in a stainless steel or glass bowl and spoon half of yogurt mixture on top, turning pork to coat. Let stand while oven heats.
Transfer tenderloin to a rimmed baking sheet, letting excess marinade drip back into bowl. Roast on middle rack for 10 minutes, turn over, pour remaining yogurt mixture over pork and continue to roast until an instant-read thermometer placed in center of pork reads 145°F, 8 to 10 minutes longer.
Set oven to broil, place baking sheet on top rack, and broil for 2 to 3 minutes, turning once, until both sides of pork are lightly browned. Transfer to cutting board, tent with foil and let rest 5 minutes before slicing and serving.