To download the LAME encoder library for MP3 files, go to Buanzo.org. If you're a Windows user, click Windows downloads; if you're a Mac OSX user, click MAC OSX downloads. On the download page, you can download the library as an executable file or a compressed file in ZIP format.
As of November 2015, the latest version of LAME encoder library for MAC OSX is version 3.98.2. It is compatible with the free audio software Audacity 1.2.5 or later running on Mac OSX 10.4 and later. The latest version of LAME encoder library for Windows is version 3.99.5, and it works with Audacity 2.0 or later.