1. Would it be correct to ask someone like a customer to lay out their problems about the product so you could help improve?- Yes, I suppose so, but it sounds a bit odd. Why not just 'tell us your problems' or 'describe your problems'?
2. To lay out your intention.-- Again, a little odd. I think 'lay out' is slightly confrontational in these contexts (1 & 2). It sounds a bit