Hope this advice isn't too late. If you've already met with the hiring manager, he obviously is very impressed with you to be inviting you to lunch with his boss and other hiring authorities.
No one person makes a hiring decision since you will be interfacing with others in their organization. So, they want to make sure you are a fit for their corporate culture.
See if you can get the names and titles of the other people who will be joining you by simply emailing the engineering director for this information. Don't make a big deal out of it. Just write, "Looking forward to our luncheon interview tomorrow. Would you be so kind as to email me back with the names and titles of your associates who will be joining us?"
Since your boss is at a director level, you likely will meet with other Directors or a VP.
People at these levels often have bios out on the web (including the company website), have published an article, or have been interviewed by the press. Research each person to get as much insight as possible as to what are their hot buttons, burning issues, or business successes.
Your second round of interviews could actually be more demanding and stressful as sometimes higher ups can play "bad cop" to see if your future boss screened you enough during the first interview. So prepare well just like you did the first time around.
A lot of candidates go into a second job interview unprepared emotionally after a great first interview, thinking since they've been invited back a 2nd time, it will be easier and more relaxed.
Lastly, even though they are taking you to lunch, this is still a job interview setting. You might want to order a light lunch because you will be doing most of the talking while everyone else is eating.