Preheat grill. Grill smoked turkey legs, turning occasionally, until just warmed through, about 15 minutes. Meanwhile, in a shallow bowl, combine onion and lime juice. Set aside for 15 minutes.
Shred meat from turkey legs. In a medium bowl, combine shredded meat, salsa verde, and cumin.
Grill tortillas for 30 seconds on each side to warm. Top each with turkey meat mixture, onion mixture, lettuce, tomato, cotija cheese, and cilantro.