Lobster palace means: An ostentatiously elegant restaurant in New York City.. The word is mostly archaic or historical; you will only encounter it in old texts, period drama, or school history rather than current teen conversation. There is no real cause for parental concern; it is descriptive vocabulary rather than risky behaviour. If your teen uses it, context will usually make the intent clear. A short, curious question about where they heard it is usually all that is needed to know whether to follow up.