Man, that image is a beautiful example of what’s going wrong. Worthy of being in a troubleshooting guide.
I looked into this a long time ago, but forgot what the different potential problems were. You should check your lightmap resolution first:
This thread might help you out as well:
https://forums.unrealengine.com/development-discussion/content-creation/19663-tottally-black-object-after-light-rebuild-etc
Also check this one:
Sorry I don’t have a direct solution for you. Does your lighting build log have any warnings/errors in it? If you can’t find any, try posting it with your question here.