Make the sauce. In a small bowl, mix mayonnaise, sour cream, lemon juice, grated garlic, salt, and pepper. Stir until smooth.
Refrigerate while you cook the chicken.
Prep the chicken. Slice chicken into thin strips. Pat dry with paper towels so it sears instead of steaming.
Season generously. In a bowl, combine minced garlic, melted butter, olive oil, lemon juice, smoked paprika, onion powder, oregano, black pepper, and salt. Toss chicken in this mixture until coated.
Cook the chicken. Heat a large skillet over medium-high heat.
When hot, add the chicken in a single layer. Cook 4–6 minutes, stirring a couple of times, until golden at the edges and cooked through. Avoid overcrowding; cook in batches if needed.
Rest and toss with herbs. Remove from heat.
Sprinkle with chopped parsley and toss. Let it rest 2–3 minutes to keep the juices in.
Warm the wraps. If using low-carb tortillas, warm them briefly in a dry skillet for 10–15 seconds per side to make them pliable. If using lettuce, pat leaves dry so the sauce clings.
Assemble. Spread a spoonful of sauce onto each wrap.
Layer shredded romaine or cabbage, sliced cucumber, and red onion. Add a generous portion of garlic chicken. Top with cheese if using and a squeeze of lemon.
Wrap it up. Fold the sides toward the center, then roll tightly from the bottom.
For lettuce wraps, simply fold the leaf around the filling and secure with a toothpick if needed.
Serve. Finish with a light drizzle of olive oil and a little extra parsley. Enjoy right away while warm.