I recently started as lead dev at a small company experiencing some real growing pains. The CEO wisely had me spend a couple days my first week going around talking to team leads. It was very productive.
I started with almost the exact same question Rachel suggests here. My version:
> What's currently frustrating you?
I deliberately left it open-ended and found many of the non-technical answers worth passing along to management. "Let the fools have their tartar sauce!":
https://www.youtube.com/watch?v=X25rP4rTw3A
The other question I came up after my first couple meetings. I called it the Magic Lamp question:
> If, as the magic genie of this company I could grant you three wishes, what would they be?
By day two, these were the only questions I needed to ask. Following up with the CEO, we came away with a very clear vision of what our development priorities needed to be. Most of it aligned with what I already sensed coming in, but there were still some useful surprises for us both.
(And, yes, found a few clever spreadsheets functioning as de-facto business applications.)