All this information has been in my first post. ;)
So this is how far I got:
I created a stream template of type "MPEG-TS Spawn/built-in" with the following command (aac 320kbps as mp3 or liblame is not available):
/usr/local/bin/ffmpeg -re -i pipe:0 -c:a aac -b:a 320k -f matroska pipe:1
Mime-Type is "audio/mp4".
This is the output:
2019-01-05 14:46:18.850 spawn: Executing "/usr/local/bin/ffmpeg"
2019-01-05 14:46:18.866 spawn: ffmpeg version git-2019-01-04-5faa1b8 Copyright (c) 2000-2019 the FFmpeg developers
2019-01-05 14:46:18.867 spawn:   built with gcc 4.9.2 (Raspbian 4.9.2-10+deb8u2)
2019-01-05 14:46:18.867 spawn:   configuration: --enable-gpl --enable-nonfree --enable-mmal --enable-omx --enable-omx-rpi
2019-01-05 14:46:18.867 spawn:   libavutil      56. 25.100 / 56. 25.100
2019-01-05 14:46:18.867 spawn:   libavcodec     58. 43.100 / 58. 43.100
2019-01-05 14:46:18.867 spawn:   libavformat    58. 25.100 / 58. 25.100
2019-01-05 14:46:18.867 spawn:   libavdevice    58.  6.101 / 58.  6.101
2019-01-05 14:46:18.867 spawn:   libavfilter     7. 46.101 /  7. 46.101
2019-01-05 14:46:18.867 spawn:   libswscale      5.  4.100 /  5.  4.100
2019-01-05 14:46:18.867 spawn:   libswresample   3.  4.100 /  3.  4.100
2019-01-05 14:46:18.867 spawn:   libpostproc    55.  4.100 / 55.  4.100
2019-01-05 14:46:25.478 spawn: Input #0, mpegts, from 'pipe:0':
2019-01-05 14:46:25.478 spawn:   Duration: N/A, start: 79417.273411, bitrate: 320 kb/s
2019-01-05 14:46:25.479 spawn:   Program 1 
2019-01-05 14:46:25.479 spawn:     Stream #0:0[0xf01](deu): Audio: mp2 ([3][0][0][0] / 0x0003), 48000 Hz, stereo, fltp, 320 kb/s
2019-01-05 14:46:25.494 spawn: Stream mapping:
2019-01-05 14:46:25.495 spawn:   Stream #0:0 -> #0:0 (mp2 (native) -> aac (native))
2019-01-05 14:46:25.508 spawn: Output #0, matroska, to 'pipe:1':
2019-01-05 14:46:25.509 spawn:   Metadata:
2019-01-05 14:46:25.509 spawn:     encoder         : Lavf58.25.100
2019-01-05 14:46:25.509 spawn:     Stream #0:0(deu): Audio: aac (LC) ([255][0][0][0] / 0x00FF), 48000 Hz, stereo, fltp, 320 kb/s
2019-01-05 14:46:25.510 spawn:     Metadata:
2019-01-05 14:46:25.510 spawn:       encoder         : Lavc58.43.100 aac
2019-01-05 14:46:26.003 spawn: size=       1kB time=00:00:00.47 bitrate=   9.9kbits/s speed=0.925x    
2019-01-05 14:46:26.504 spawn: size=      33kB time=00:00:00.98 bitrate= 274.3kbits/s speed=0.973x    
2019-01-05 14:46:27.013 spawn: size=      33kB time=00:00:01.49 bitrate= 180.3kbits/s speed=0.984x    
2019-01-05 14:46:27.520 spawn: size=      65kB time=00:00:01.98 bitrate= 270.4kbits/s speed=0.98x    
2019-01-05 14:46:28.021 spawn: size=      65kB time=00:00:02.49 bitrate= 215.0kbits/s speed=0.988x    
2019-01-05 14:46:28.525 spawn: size=      98kB time=00:00:02.98 bitrate= 268.4kbits/s speed=0.986x    
2019-01-05 14:46:29.034 spawn: size=     130kB time=00:00:03.49 bitrate= 304.3kbits/s speed=0.989x    
2019-01-05 14:46:29.546 spawn: size=     130kB time=00:00:04.01 bitrate= 265.4kbits/s speed=0.991x    
2019-01-05 14:46:30.040 spawn: size=     163kB time=00:00:04.50 bitrate= 296.1kbits/s speed=0.99x    
2019-01-05 14:46:30.554 spawn: size=     163kB time=00:00:05.03 bitrate= 264.8kbits/s speed=0.996x    
2019-01-05 14:46:31.063 spawn: size=     195kB time=00:00:05.54 bitrate= 288.6kbits/s speed=0.997x    
2019-01-05 14:46:31.447 spawn: av_interleaved_write_frame(): Broken pipe
2019-01-05 14:46:31.476 spawn: Error writing trailer of pipe:1: Broken pipe
2019-01-05 14:46:31.476 spawn: size=     195kB time=00:00:05.93 bitrate= 269.9kbits/s speed=0.991x    
2019-01-05 14:46:31.476 spawn: video:0kB audio:227kB subtitle:0kB other streams:0kB global headers:0kB muxing overhead: unknown
2019-01-05 14:46:31.479 spawn: [aac @ 0x1bd0990] Qavg: 24347.391
2019-01-05 14:46:31.479 spawn: Conversion failed!