Are you writing about a Cloud version (this forum) or a standalone version?
An upgrade installer will USUALLY allow you to enter the serial number for a previous version
Help for Download & Install & Setup & Activation
Welcome to Adobe Forum,
The previous version does not need to be installed on the computer on which you are installing the upgrade.
At the time of install, it will ask you the previous version that you own, you have to choose the previous version, then it will ask you to enter that serial number for installation to complete.
I got it.
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Please use a web browser to edit your reply #3 and remove your personal information... this is an open forum, not Adobe support
This does not work for me. I'm upgrading from Lightroom 5 to 6, putting the newer version on a new computer. I select LR 5 as previous version, give the serial number, which it accepts but it tells me that I don't have the previous version on this computer.