Audacity is a good program for recording sound and editing. If you want to then save as MP3 then, yes, you need to download Lame, which is just a little program.
Once you download Lame, make note of the path to that file, ie probably in Downloads and when you click, in Audacity, to export/save as MP3, it will ask the location of the Lame file and give you the wherewithall to point to it.
More than that, I don't know. I'm not into editing music particularly but do save as MP3 for my purposes.
Hope this helps