When I was at Nike I frequently had lunch or coffee with different VPs, even as a just a staff designer. In my experience they were all happy to do it and I got to ask a ton of questions and better understand their thought process. What I came to realize is that they had just as many questions for me on moral, how certain initiatives were perceived, and how they could do better.
On our way to lunch once one of the directors passing by asked the VP why he always went to lunch with me. The VP’s response was “he’s the only one that ever asks.”
The old Ray Charles quote applies, “If you ask, the worst they can say is no.”
To slippyfish’s point. Ask the VP in passing if you can have lunch sometime and then follow up with his or her admin, so the admin knows the VP wants to do it.