Disc version or serial number

A Creative Cloud subscription is the only option to remain current with Light Room releases. The last stand-alone version, LR6, is no longer supported by Adobe. Here's a post on the reasons why Light Room Classic (Creative Cloud) is preferable:

https://shotkit.com/lightroom-6-vs-cc/

I agree with my fellow members that the general answer us no.

And arguing with Adobe will get you nowhere. They have legal and moral rights to not support sunsetted (end of life) software. And if you read your end users license agreement, you will find language to that. (use actually never payed fir ownership, you really paid for use, and support dies 3 years after end of life of the program)

AS TO MY POINT

What version do you have now?

What version do you want to upgrade to?

If you have Lr  v6 older than v6.14 ( six point fourteen), and you want to update to 6.14, state so, one if the members may have a backdoor non Adobe link.

If you have Lr v5 or older, then no. That would require a new license, and those perpetual licenses are no longer sold. 

If you have Lr v6 or older and want to upgrade to Lightroom Classic v10.4, no no no.

Second Point

If you have, say v6.14 and you want new features such as new cameras, new functions, etc. Then no.

There is no one time single purchase version of Lightroom available anymore. Lightroom 6 was the last such version, and Adobe stopped selling it several years ago. If you want the current version of Lightroom that works similarly to Lightroom 6 is called Lightroom Classic. It is available in the Adobe photography plan bundled with Photoshop. The subscription cost is $9.99/month in the US. Adobe support has basically been outsourced and is not particularly accessible. But if you want to try a live chat then here is the link.

Contact Customer Care (adobe.com)

Click on the circle in the lower right-hand corner to initiate a live chat conversation with an Adobe support person.

I was wondering if Adobe still has the option to just upgrade with a one time fee

Depends on what software you are talking about.

As far as I know, Photoshop Elements is still a one time fee. The rest are subscription only.