Let apt make your life easier:
If you are new to Linux, I do not suggest installing texlive from their homepage. That process is very easy, but the problem is that whenever you install anything with apt that depends on a texlive package, it won't recognize that you already have texlive installed. I'm pretty sure that Ubuntu 12.10 comes with texlive 2012 in the repos so I would suggest installing it from apt. If you have a lot of space and don't want to deal with missing packages:
sudo apt-get install texlive-full
But if you just want the basics you don't have to install all of that. You could just do:
sudo apt-get install texlive
In summary, apt makes sure that all of the packages and programs on your computer play nice with each other. Installing manually introduces a new kid to the playground that doesn't necessarily play by the rules.
Finally, reconfigure LyX so that it is aware of your new toys:
Start LyX and go to Tools > Reconfigure