Udo, the reason Audacity "MP3 Files" export now requires LAME compiled by us is that we have to support correct reported file length and metadata (like tracks, artist and genre) in as many applications as possible. When people used any LAME version they liked, we used to get a lot of complaints that reported length and metadata was wrong. When we make changes to improve that, the changes must be against latest LAME, so they won't work if people have got ancient versions of LAME.
Your real issue is with LAME so why not post your example files to the
LAME developers list ?
Audacity Beta can link to any command line version of LAME you like if you choose "(external program)" when you export instead of "MP3 files". The default command will give you 128 kbps constant bit rate (CBR). I tested out LAME 3.90.3 that way on Windows (you just put have to put lame.exe from any Windows bundle of LAME in Program FilesLame For Audacity). Your file sounds much better with 3.90.3.
I can confirm 3.98.3 is no improvement if you export at the default 128 kbps CBR. I got a considerable (and expected) improvement by making the file mono at Tracks > Stereo Track to Mono, and exporting at 128 kbps CBR. I also got considerable improvement by clicking Options and exporting at variable bit rate 6 (95 -135 kbps). The resulting file is still only 131 kbps but clearly uses more bits for the first part of the note and doesn't waste them on the end where it dies away into the noise.
If you want to pursue command line encoding, I believe the command line encoder wants "LameLib" that you can get from a bundle like
this for LAME 3.91. I would try the LameLib inside LameLib.bundle.zip. Put it in /usr/local/lib/audacity.
If LameLib from that bundle gives output errors, you can get
LAME 3.93 from Sourceforge and compile lame from the "mac" folder.
Gale