Lug-Nut is mentioned by Sierra Petrovita when asked more about Ronald Laren. She will start talking about how tough Ronald is and will mention Lug-Nut and two other raiders. The two unknown raiders were killed by Ronald, who then punched Lug-Nut in the face.
Grady's Package: Lug-Nut appears and confronts the Lone Wanderer as soon as they loot the naughty nightwear. At this point, the Lone Wanderer can give him the naughty nightwear, kill him, or pass a speech check resulting in Lug-Nut backing off.