Trim fat from lamb. Combine 2 cups onion and next 6 ingredients (onion through thyme) in a large zip-top plastic bag. Add lamb to bag; seal. Marinate in refrigerator 2 hours, turning occasionally. Remove lamb from bag; discard marinade.
Preheat oven to 350°.
Place lamb on a broiler pan; insert meat thermometer into thickest portion of lamb. Bake at 350° for 1 hour or until thermometer registers 145° (medium-rare) to 160° (medium). Let stand 15 minutes. Slice lengthwise into thin strips.
Spread each pita with about 2 1/2 tablespoons Yogurt-Tahini Dip. Divide lamb, red onion, mint, tomato, and pickles evenly among each pita; roll up. Serve immediately.