Combine ground lamb, onion, garlic, yogurt, breadcrumbs, salt, pepper, cumin, paprika, oregano, coriander, and cayenne in a large bowl. Mix by hand 2-3 minutes until sticky. Cover and chill 30 minutes.
Roll It Thin
Divide into 3-4 portions. Roll each between parchment sheets into a 12x15 inch rectangle, about 1/8 inch thick.
Roll Into a Log
Remove the top parchment. Roll tightly from the long side into a flat log. Repeat with remaining portions.
Bake
Bake at 400°F for 22-25 minutes until deeply browned and 160°F internal. Broil 2-3 minutes for extra-crispy edges, if you like.
Rest and Unroll
Rest 3-5 minutes, then peel back the parchment. The meat unrolls into a crisp sheet.
Chop and Assemble
Chop into bite-sized pieces. Fill warm lavash with garlic sauce, lamb, cabbage, tomato, parsley, chili flakes, and lemon juice.
Notes
Squeeze excess liquid from the grated onion before mixing, too much moisture keeps the roll from browning.
Chill the meat before rolling, it holds its shape and rolls out clean.
Pull at 160°F exactly, ground lamb dries out fast past that point.
Make ahead: roll raw logs up to 1 day ahead, refrigerated, or freeze up to 2 months.