Seriennummer suchen

A correct answer is given here: https://community.adobe.com/t5/lightroom-classic-discussions/where-can-i-find-my-license-key-in-lightroom/td-p/6803290

I would imagine it applies to Lr 6 as well.

Please do yourself a favor, devise a way to keep track of your serial numbers (not just for Lightroom but for all the software you own) so you are never again in the situation where you don't know your serial number. I do it by saving that information in a file on my computer that is easy to find, and then also making sure I have backups of that file.

I'm looking for the serial number of my installed Lightroom copy on my computer. Is there a place where I can find them?

Lightroom Classic doesn't use a serial number.

Are you using an older version? If so, what version number?