Slice chicken breasts against the grain into ¼-inch thick strips, ensuring uniform thickness for even cooking.
In a medium bowl, combine lime juice, 2 tablespoons avocado oil, cumin, chili powder, smoked paprika, oregano, 1.5 teaspoons salt, and black pepper. Add sliced chicken and toss to coat thoroughly. Allow to marinate for 30 minutes at room temperature (or up to 4 hours refrigerated).
While chicken marinates, slice bell peppers and onions into uniform ¼-inch strips. Mince garlic and set aside separately.
Place cast iron skillet over medium-high heat and preheat for 5 minutes until surface temperature reaches approximately 375-400°F.
Using tongs, remove chicken from marinade, allowing excess to drip off. Cook chicken in a single layer (in batches if necessary) for 2-3 minutes until browned, then flip and cook additional 1-2 minutes until internal temperature reaches 165°F. Remove to a clean plate and tent with foil.
In the same skillet, add remaining 1 tablespoon avocado oil. Add peppers and onions, sprinkle with remaining salt, and cook over medium-high heat for 4-5 minutes, stirring occasionally. Add garlic during the final 30 seconds of cooking.
Return cooked chicken to skillet with vegetables, including any accumulated juices. Toss gently to combine and heat through for 1 minute. Remove from heat.
Warm tortillas in the hot skillet or separately, and serve immediately with fajita mixture and desired accompaniments.