If you have purchased an S1, S2 or S3 license, you can unlock LFS using your LFS username and GAMEpassword.
If you have not yet set a GAMEpassword or have forgotten it, you can set it on your account details page .
On the first screen of LFS after you start it up, there is an "Unlock Live for Speed S3" button, which takes you to the unlock screen. There, enter your LFS username and GAMEpassword and press the Unlock button at the bottom right of the screen. Provided you've entered the correct username and GAMEpassword and provided you are connected to the internet, LFS should unlock.