The matrix looks fine, but the "LFMIX" stream stuff not so much. I'm not sure there is really any need for that, as you could set the BASS_SPEAKER_FRONTLEFT flag on the mixer itself and make it mono. The code could be modified to look like this...
HSTREAM mixer=BASS_Mixer_StreamCreate(44100, 1, BASS_SPEAKER_FRONTLEFT); // create a mono mixer on front left speaker
HSTREAM source1=BASS_StreamCreateFile(FALSE, file1, 0, 0, BASS_STREAM_DECODE); // open 1st source file
BASS_Mixer_StreamAddChannel(mixer, source1, BASS_MIXER_MATRIX); // add it to the mix with matrix mixing enabled
float matrix[1][2]={
{0.5, -0.5}, // mono out = left - right in
};
BASS_Mixer_ChannelSetMatrix(source1, matrix); // apply the matrix
BASS_ChannePlay(mixer, FALSE); // play the mix