HI van plancken,
Assuming that you are using a creative cloud subscription when you will sign in to new machine, it will give you the option to sign out from previous machine/machines.
and how to sign out?
I am using adobe Lightroom 6.2.1
When you will sign in , it will you the dialog box there to sign out from other computers so you just need to hit sign out button.
If that doesn't give you the option and still you are not able to sign in then please contact our support team : https://helpx.adobe.com/contact.html