Best to break this down piece by piece.
Can you quantify what images were not copied? Raw files, JPEGs, PNGs, or Aperture previews?
Lightroom does not support some file types, end of story. In my tests, all raw files were copied, but most Aperture previews were not.
Lightroom stores images using it's own method. As with Aperture, remember you'll need to separate the physical storage from the organization in your library (Aperture) /catalog (Lightroom). Aperture abstracts physical storage, Lightroom does not. Aperture uses "managed" and "referenced" techniques for storage of any one image, and both coexist within the library.
You should have your projects maintained some semblance of order when converting to Lightroom. All your projects should be defined in your Lightroom catalog. But if I remember correctly, they all end up on one level in Lightroom. But if you want a deep hierarchy, you'll need to use a technique described below. And if you chose, the albums should have been copied over as well. Smart Albums will not come over.
Star ratings and keywords should have come over. Have not heard reports of issues here, other than keyword hierarchy and inconsistent labeling of keywords, whether they be original images or Aperture previews.
You may want to try copying your library and images to this external drive as a pre-conversion task, and relocate all your images, choosing options to create a deeper file structure that includes project name, date format, etc. I posted a response to another user who wanted to do the same thing. This approach is the only way to keep a hierarchy of projects, and you're subject to the abilities in Aperture to do so. The Lightroom import plugin will not do it for you.