Place the chicken into a sealable bag. Place the peppers and onion into a separate sealable bag. Add the olive oil, lemon juice, chili powder, ground cumin, cayenne pepper, salt, pepper, and garlic to a jar with a screw top or tight fitting lid. Shake until well combined. Pour 1/3 over chicken, 1/3 over vegetables and reserve the remainder in the jar for using when cooking the chicken fajitas. Seal the bags tightly and refrigerate for one hour to overnight.
When ready to cook, heat a large skillet over medium-high heat. Pour vegetable bag into the skillet and cook until just tender crisp, about 5 minutes. Remove the vegetables from the skillet to a plate and add chicken strips to the same skillet. When the chicken is cooked throughout, add vegetables back to the skillet along with the reserved marinade.