(written from a Production point of view)
In a deleted scene from Star Trek: First Contact actor James Mapes appeared as Buster, a drunk in the Dixon Hill holographic program. In this scene Buster grabbed Lily's arm and asked her if she wants a drink. Lily reacted angry and pushed him away. Jean-Luc Picard, in the role of Dixon Hill, told him "Watch your hand, Buster. She's with me" and he walked away.