Place steak in a large heavy duty zip top plastic bag; add steak sauce and pepper.
Seal bag; chill 30 minutes turning once.
Remove steak from marinade, discarding marinade.
Mash avocado in a small bowl.
Stir in lemon juice and remaining ingredients; cover and chill Grill steaks, covered with grill lid, over medium-high heat (350 to 400 degrees) 7 minutes on each side, or to desired degree of doneness.