Start the meeting in your office, one hour earlier, so you make progress and go to lunch with momentum. Both meetings will sparkle that way.
Plan what you want to accomplish at the premeeting and the luncheon. Improvisation is for the theater and doesn't work there that often. Don't rely on it for a business meeting.
Think charm alone can make a lunch meeting successful. Charm lasts for five minutes. The lunch will take an hour-and-a-half. Plan it out and have an agenda.
Expect to get it all done at lunch. Instead, start with a one-hour office meeting. Then the lunch part will be really productive.
Use a business lunch to try out a new restaurant. Egad, that's so foolhardy it deserves to be punished. And it will be.