Are lemonade stands illegal in the US?

Honestly it's a bit of a grey area. If it is on your own land, no. If it's on private land and you have permission, no.

If it's on Public land and you don't have the relevant permits... Yes.

If you are an adult you will almost certainly be moved and you risk a fine.

If you are a child you still might get moved but nothing more. No self-respecting local authority will punish a child, but they may (quite rightly) ask you to move on.

For more debate check out - http://www.lemonade-stand.co.uk/blog/do-i-need-a-permit-to-start-a-lemonade-stand/