So avconv is available as a package for raspbian, but I couldn't get it to work with my livestreamer command line out of the box (still testing on a ubuntu machine). I decided to compile ffmpeg on the RPi as per these instructions:

http://www.jeffreythompson.org/blog/2014/11/13/installing-ffmpeg-for-raspberry-pi/

Compiling x264 seemed to work just fine.

ffmpeg: cloning took quite some time. As the instructions mention that it can take a "REALLY long" time, I decided to time the make command just to have a number. I also used all four cores (make -j4). The result: 333 minutes, and the "recipe for ffmpeg_g failed". ffmpeg seems to work, though (executing it without arguments on the command line doesn't throw error messages), so I don't really care about that.