You need a Second Adobe ID that is not tied up with an Adobe Creative Cloud subscription. Once you create and sign in to that second Adobe ID it will ask for the serial number for the stand alone version.
Not sure if you can do that now without doing a complete uninstall of LR on your home system.
That is exactly what is written in the article I linked.
And yes, it should work without a uninstall.
What I meant was now that the OP has Signed in with a valid subscription based Adobe ID LR may not open or open enough to change the sign in name. Giving an error that this App is already running on 2 computers.
If the OP had not already installed it on 2 other computers and signed in on those other 2 computers then No problem Signing out and back in on the home system using another, different, Adobe ID not associated with the subscription system.