Out of country purchase

You should be able to download the software without making a purchase, as the purchase is merely a serial number used the activate the software after the short trial period has expired.

LR 6 can be downloaded from here.  First download the large application installer and run it, then download and run the latest update 6.14:  https://helpx.adobe.com/download-install/kb/lightroom-downloads.html

As far as buying software in South Korea, the issue may be that while South Korea is not on the list of embargoed countries like Russia or North Korea and Iran and others are, it is on the Restricted Parties list, which I think means individuals or companies there are restricted from making purchases from (some) US companies, and I would speculate that Adobe has no way to prove identity to know they aren't selling to the individual or company so they just deny sales to everyone in that country.  I don't know if that is truly the case, but it would make sense.  I would expect Amazon to have the same restriction but perhaps they don't.

Adobe also is picky about shipping software to a different country compared to where the Adobe ID was created due to needing to collect the correct amount of taxes.  This prevents people from registering in a country that has somewhat lower taxes like the US but shipping to a country in the more socialist EU that has higher taxes.  There are some ways around this by creating a new Adobe ID and using that to purchase and register the software.

One worry I would have is that even if you got a serial number somehow, new Adobe ID, someone buys elsewhere and emails, etc, that the serial number would not be accepted during the activation process, or Adobe would eventually decide to revoke the serial number.  They are pretty particular about taxes and piracy and sometimes it takes some time for them to decide.  Obviously your situation is not illegal or otherwise bad, but it's hard for a large company with millions of customers to have policies and rules that are precise enough to allow the correct people to purchase.

Here is the list of countries with various export controls:

https://doresearch.stanford.edu/research-scholarship/export-controls/export-controlled-or-embargoed-countries-entities-a…