The software patent on LAME encoding library has expired, so now the LAME library for MP3 export is built-in with Audacity for Windows and Mac. Linux users will still need to download and install the free and recommended LAME third-party encoder to export MP3 files from Audacity.
Linux users should use the following instructions to download and install the free and recommended LAME third-party encoder to export MP3 files with Audacity.
Windows: LAME is now built-in with Audacity for Windows.
Mac: LAME is now built-in with Audacity for Mac.
Linux/Unix: See the LAME installation section on Installing and updating Audacity on Linux.
I downloaded Audacity on a friends Windows PC yesterday, and it allowed me to export MP3 without asking for any other steps!
From Audacity’s website: