That app does not do it all for you automatically. It does some preparation in Aperture and duplicates your entire picture collection.
Valerio, Adobe’s guide does say you should simply import your files into Lightroom. However, they must be in regular folders - "referenced" rather than "managed". See my Moving from Aperture to Lightroom for more detail.
Thank you John for your answer (and also thanks to Jao).
I will try to migrate as the John's guide explains.
I also hope that Adobe will release an automatic tool, however.
Adobe announced yesterday that they are working on an automatic tool. So what you might do is process all new pictures in Lightroom and leave older pictures in Aperture until the tool is released.