Classic Beef Fajitas

1A. FOR A CHARCOAL GRILL: Open bottom vent completely. Light large chimney starter mounded with charcoal briquettes (7 quarts). When top coals are partially covered with ash, pour evenly over half of grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.
1B. FOR A GAS GRILL: Turn all burners to high, cover, and heat grill until hot, about 15 minutes.
2. Clean and oil cooking grate. Pat steak dry with paper towels and sprinkle with lime juice, salt, and pepper. Place steak on grill (hot side if using charcoal) and cook (covered if using gas) until well browned on first side, 4 to 7 minutes. Flip steak and continue to cook until meat registers 120 to 125 degrees (for medium-rare) or 130 to 135 degrees (for medium), 3 to 8 minutes. Transfer steak to carving board, tent loosely with aluminum foil, and let rest for 10 minutes.
3. While steak rests, place onion rounds and peppers (skin side down) on hot side of grill (if using charcoal) or turn all burners to medium (if using gas). Cook until tender and charred on both sides, 8 to 12 minutes, flipping every 3 minutes. Transfer onions and peppers to carving board with beef.
4. Place tortillas in single layer on hot side of grill (if using charcoal) or turn all burners to low (if using gas). Cook until warm and lightly browned, about 20 seconds per side (do not grill too long or tortillas will become brittle). As tortillas are done, wrap in clean kitchen towel or large sheet of foil.
5. Separate onions into rings and slice peppers into 1⁄4-inch strips. Slice steak, against grain, 1⁄4-inch-thick. Transfer beef and vegetables to serving platter and serve with warmed tortillas.