I was wondering if -a and -m m in LAME do the same thing. If not, what's the difference?

-a: mono channel = (l+r)/2
-mm: mono channel = l

I just found this page: http://lame.cvs.sourceforge.net/*checkout*.../switchs.html#m

Does it mean that the page is not accurate? For both -a and -m m it states that "The downmix is calculated as the sum of the left and right channel, attenuated by 6 dB"

OK, just did a test: I generated some noise with Audition. The first 10 seconds are noise on the left channel only, the other 10 seconds are noise on the right channel only. I exported the data as stereo PCM Wave file and encoded with LAME using both -a and -m m. Both files are the same (=identical). If -m m would encode left channel only, wouldn't this mean that the resulting MP3 would have noise on both channels for 10 seconds and then 10 seconds of silence (because the last 10 seconds are noise on the right channel only)?

Well, it makes some difference if you feed in RAW PCM into LAME:
-a will downmix (l+r)/2
-mm will tell LAME there is only one channel

With stereo input from wave files, you see some message about "autoconverting from stereo to mono" passing by, LAME adds "-a" automatically.

I am wondering if fb2k pipes data as raw PCM or if it also sends the header.

Edit: Seems that with fb2k, -a and -m m also produce the same result so it doesn't pipe raw PCM. Anyways, I switched to -a just to be safe.

foobar2000 also has a DSP which converts an audio stream to mono which might be useful in your case