Mix all fajita seasoning ingredients; store extra in a sealed jar.
Toss chicken strips with olive oil, lime juice, and 2 tbsp seasoning. Marinate 30 minutes (or up to 24 hours refrigerated).
Heat a cast-iron skillet over high heat until smoking; add oil.
Sear chicken in a single layer 2–3 minutes per side until browned and 165°F inside; transfer to a plate.
Char peppers and onion undisturbed 2 minutes, then toss and cook 4–5 minutes until crisp-tender; add garlic last 30 seconds.
Return chicken to the skillet; squeeze lime over; toss 1 minute.
Warm tortillas; serve sizzling with toppings.