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Go here: Software & Services
Scroll down to Lightroom and click on 'Buy' on the right side (DO NOT click on Lightroom on the left). You may have to select a different setting in the drop-down box at the top to see Lightroom.
Select the upgrade version and your language ... et voila.
To clarify: The CC and the Standalone version are both the same application and are installed locally. For the CC version, connection to the net is needed once every month only, to verify your subscription status.
I also could not find it on the website. They're sneaky. I ended up chatting online with a rep and they right away just sent me the link to Lightroom 6 as a standalone or upgrade. Just use the drop down menu to see the options