I have tried to download Lightroom 6 onto my second computer which is a Macbook Pro, it pulls up Adobe Application Manager but Lightroom is no where to be found.. I have searched my documents, applications, finder.. EVERYTHING!
Would you please paste the screenshot of the Adobe Application Manager dialog box here so that we can help you in a better way.
Also try to reinstall Lightroom 6 from the below link:
Retrieving data ...