I am working with OS X 10.9.5, I have Audacity 2.1.0, and I am not sure if I used the .dmg or .zip installer. All I did was drag the icon into applications and later double-clicked to start installing. I tried recording, and as I attempt to save a project, I get a message suggesting to save as an audio file, I have to export to a disk. When I try to do that, I get a message suggesting that the file has to go through the Lame library. Even after downloading the Lame library, I am unable to access it and cannot save or export to create sound files in MP3, WAV or other needed formats. I am not sure what to do next.
It sounds like the install is confused.
Drag it to the trash.
Get the Disk Image (dmg) for Audacity 2.1.3 from here.
When it shows up on your desktop, double click it and it should open up into an installer. Drag the program graphic to the applications graphic.
I think the last time I did this, I dragged it into the “real” /applications folder. Either one.
Audacity projects are not audio files. When you went to save your project, Audacity warned you that you were saving an Audacity project, not an audio file that can be played in, for example, iTunes. Please see Managing Audacity Projects in the manual.
When you export the contents of an Audacity project you have a choice of formats. Please see Exporting Audio in the manual.
You only need LAME if you want to export to MP3. You can export to AIF or WAV (without the LAME library installed) and have iTunes convert to MP3 for you. If you want to export to MP3 from Audacity you need to do more than just download the LAME installed - you need to run the installer. Please see Installing LAME in the manual. You should not have any trouble exporting to AIF or WAV as those exporters are built in to Audacity.
I think there’s probably nothing wrong with your installation, but I recommend that you download and install Audacity 2.1.3 from the URL that Koz gave you.