I tried to download LR6 standalone version to my second computer three times today. It seemed to run normally, but everytime after the download was finished I got error message "Failed". The second computer has Windows 8.1 64bit system and it is actually newer and more capable than my nr.1 computer, so there should be no problem. I purchased LR6 in April and have had it running only on one computer so far so I should be able to to download it to this second computer also.
You can get Lightroom downloads for Windows or Mac from the following link together with system requirements.If it works, use the help menu to update to 6.1
To download click here to start