The default desktop picture for each new space is that of Space 1. While I haven't found a quick way to apply the same picture to multiple existing spaces, you could

1. Set the desired picture in the first space,
2. Remove all subsequent spaces, and
3. Add the spaces back in. They’ll take on the picture you set.

This is kind of a lame solution, but it’s all I’ve found. If anyone has a better way, we’d love to hear it!

I want to do the reverse: I want to know what to do in Lion so that the same desktop appears on all spaces, no matter how many I create.

That's simple: just remove your existing spaces, set the picture you want on Desktop 1, and all subsequent desktops will use that picture unless you set them otherwise.