You can buy LR without have any license from a previous version. But you have to buy the Full version which cost more money.
If you have a previous version of LR and it was installed on your present or older computer that you still have access to you can find the serial number in a TEXT file on the hard drive.
You can not buy Lightroom.
You can subscribe, as it is now part of Creative Cloud.
What country are you in?
Thank you for correcting me.