Sauté the chicken in a medium saucepan over medium-high heat for about 20 minutes. Add the vinegar, lime juice, sugar, salt, pepper, green onion, garlic, and oregano . Simmer for an additional 10 minutes.
Heat a cast iron skillet over medium heat. Place a tortilla in the pan, hot, and turn it over to heat the other side. Repeat with remaining tortillas .
Serve lemon chicken mixture on warm tortillas topped with tomato, lettuce, cheese and salsa.