If you buy an S2 license you will be able to unlock any version of LFS S2 and have access to all content. Buying an S2 license does not affect your ability to connect to internet races as such. If you can't connect to online races in demo mode, this will not change even if you have a license.
What you really want to do is this:
1) Download the latest version of LFS from
http://www.lfs.net/?page=downloads
2) Configure your software firewall to allow LFS to connect to the internet
3) Check if you can get online with LFS. If you can, go to step 7
4) If you can't, configure your router's firewall to allow LFS access to the internet
5) Repeat step 3
6) If you still can't connect to online races, seek professional advice. Note, that if you're on a work/school LAN you may not be able to play LFS online period.
7) Buy license
8. Unlock
9) nJoi
If you have some strange legacy version of LFS and you unlock it with your license, you will have to unlock again when you update to a recent version of LFS.