I was having the same problem as you with OS 10.6.3 there is no way to load the .dmg file into the correct /usr/ folder. When you run the installer it says that it installed it successfully but the file simply disappears. I checked the contents of the folder from Terminal and it is not there. Here's what I did to get it working:
go to:
http://wiki.audacityteam.org/index.php? ... stallation
look for a link for "libmp3lame-osx-universal-3.97.zip"
Download the .zip file (even though it says that it's for an earlier OS version).
Double click to unzip it.
In the folder that opens up, open the folders package -> usr -> local -> lib -> libmp3lame.dylib
Move the libmp3lame.dylib file to any place on your computer (the desktop is convenient)
Now when you do an export and go through the dylib installation process you can browse for it and direct the installer to the right location (e.g., desktop) and it will find it and install it where it needs to be.
After installing it, to be sure quit Audacity and restart it. Now you should be able to use the mp3 export feature. Simple as that.
I don't know why the .dmg file installation does not work but you can pretty much forget all the instructions in the installation page because for 10.6.3 it does not work.
I hope that helps, and if it did I've done my good deed for the day and payed back for the application with a little Beta trial feedback.