Once pictures are in Lightroom, only move them in Lightroom, not using Finder/Explorer. That way it won't lose track of them.
If the external drive isn't already shown in LR, move one image in Finder/Explorer and fix it the way Michael suggests (trouble with that method is you have to fix one folder at a time). This makes the folder appear in LR and you can then drag the rest of the pictures across.
Also look at storing XMP files with the keyworded images.
Try the workflow out with a few pictures first.