Purée cucumber, yogurt, lemon juice, garlic, salt, and pepper in a blender until almost smooth, about 1 minute. Stir in mint and chill, covered, until serving.
Preheat broiler.
Wrap pitas in foil and put in lower third of oven to warm while broiling lamb.
Put lamb on oiled rack of a broiler pan and sprinkle with salt and pepper. Broil lamb 5 to 6 inches from heat, turning over once, 12 to 14 minutes total for medium-rare.
Transfer to a cutting board and let stand 5 minutes, then thinly slice.
While lamb is standing, toss together salad ingredients in a bowl and season with salt and pepper.
Stuff warm pita pockets with salad and lamb, then drizzle filling with tsatsiki sauce.