"Take you to lunch" is a common phrase in American business (and social relations in general). The taker buys lunch for the taken.

The implication is that the taker is making life easy for the taken, all the taken has to do is show up.

Thanks for the information about this American business phrase. The implication on an invitation is that who invites is trying to sell you something (there is no free lunch in business).

Your correct that it is often a situation where the taker is selling. It can also be an expression of gratitude for a favor.

However, there is another business scenario in which a mentor uses lunch as the opportunity to schedule time with their mentee. Sharing a meal often provides a less formal setting and fosters the personal relationship.

This case appears to be a combination of the second and third scenarios.