Can I restore a Snow Leopard backup onto a Lion machine?

Question

So I am a little confused and slightly worried, and I was wondering if someone could answer this.

I have a Time Machine backup saved on an external HD for my Mac mini that is running the latest version of Snow Leopard.

If I buy a new computer running Lion, will there be issues with using my Snow Leopard back-up to put my files on the new machine running Lion? Is that even possible? Or do I have to update my old computer to Lion first, and make a back-up before moving to the new computer?