It is not a lottery as the green card lottery but if you are of European descent there is the chance you can apply for citizenship. Look out for Italian, Spanish, Hungarian and Irish ancestors in particular.

Edit: This scheme is ridiculously complicated in the EU and I know of no coherent source. If anyone is specifically interested in having the right of abode to work in the EU, contact me with a hint to family history and we can work something out. In the interest of the community I urge you to do this publicly.