I did several tests recently with a few audio samples ( mostly created by sox ) - the one I would like to talk about is a 19.3kHz tone @ 48kHz.
when I apply a 20.1kHz or lower low-pass filter, there is a ton of "noise" is the resulting mp3, if I do the same with 20.2kHz low-pass or higher, it is >>much closer<< to the original.
I used 'baudline' and "my ears" to compare the results.
This case applies to Lame 3.99.5 and 3.98 - did not perform any tests on other Lame releases. ( compared to number of vorbis, aac, flac encoding results without a single case that matched or was similar to Lame )