Converting from stereo to mono will mean re-encoding, so keeping the same bit rate would be meaningless. In fact, converting a 128 kbit/s MP3 -> a new 128 kbit/s MP3 will net you godawfully terrible quality, even if the second one is mono (and therefore requires a lower bit rate for the same subjective quality).
Generally, I would use a Variable Bit Rate (VBR) setting for MP3, which targets a specific quality and lets the encoder set whatever bit rate is required (completely silent audio needs a lower bit rate than whalesong, which needs a lower bit rate than dubstep). From the command-line, ffmpeg can convert audio to mono with the option -ac 1, like so:
ffmpeg -i input.mp3 -c:a libmp3lame -q:a 2 -ac 1 output.mp3
See this page for a guide to using -q:a. Note that the table on that page is aimed at stereo audio; the actual bit rates you'll see will be somewhat lower. Normally, I recommend 3-4, but since you're encoding from MP3s rather than an original CD, you should aim a bit higher.
This can, of course, be automated very easily. On Linux/OSX/other UNIX-like, to convert a directory of MP3s:
for f in *.mp3; do ffmpeg -i "$f" -c:a libmp3lame -q:a 2 -ac 1 mono-"$f"; done
To do so recursively:
find . -type f -name "*.mp3" -exec ffmpeg -i '{}' -c:a libmp3lame -q:a 2 -ac 1 mono-'{}' \;
If you have GNU Parallel and a multi-core machine, you may find this useful:
find . -type f -name "*.mp3" | parallel ffmpeg -i {} -c:a libmp3lame -q:a 2 -ac 1 mono-{}
The answer to my own question is: No - it is not possible with lame
My work-around solution is to use the command-line tool sox and do the channel duplication prior to mp3-conversion:
sox mono.wav -c 2 stereo.wav
Then afterwards use lame:
lame -m j stereo.wav stereo.mp3
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