I'm familiar with lean methodology and aware that ideas don't really mean much, but at the same time I'd like to work on some big problem that's compelling. I know that I'll probably pivot a lot but just to start out what general problem would you reccomend I try and solve?
I'd have to concur with Steve Mason's answer above. You can sit around and try to brainstorm big problems, but you are limited to what you personally have been exposed to and can relate to. Getting involved with contracting or consulting will give you insight into many different environments that you normally would not have known existed. Try to determine what industry you truly have interest in and start there. Get involved with everything and anything you can within that industry (e.g. associations, developer groups, contracting, etc). As you become more and more involved with that industry, you'll start to understand the nuances of the participants and the mindset. From there, you can start to really focus your efforts on uncovering the best opportunities to address.