Did you try right-click over the installer and running as Administrator?
Did you try the older zip file “libmp3lame-win-3.98.2.zip” on http://lame.buanzo.org/#lamewindl? Download that zip, right-click and choose “Extract All”. Extract to some folder you have permission to write to, like your Desktop. Then Edit > Preferences… in Audacity, choose the “Libraries” section on the left, then in the “MP3 Library Version” section, press “Locate…”. Then select and open the “lame_enc.dll” file in the folder you extracted that file to.
Well, you may not like the reply… I was playing with Windows Media Player, (I’ve recently bought a new desktop, so it is a later version than I had), and I found I can rip a CD and save as MP3 very quickly and simply. Didn’t like to tell you that in my last message.
(It was all legal; it is a CD I bought and wanted to put onto my MP3 player)