1. Download LAME.
2. Compile it.
3. Install it.
4. Delete LAME from inside the package contents of iTunes-LAME.
And that's it. iTunes-LAME will then use the newest version of LAME.
If you don't understand how to do any of steps 1 thru 4, I can provide
more details.
Keep following the initial 4 steps I gave you and it will work.
When you delete LAME from inside the package contents of iTunes-LAME,
it will automatically use the one you just installed (in /usr/local/
bin).
Maybe someone else knows of specific examples of apps that use the
LAME libraries installed?
I'd leave LAME where it belongs :)