You should be able to compile xLights on the BBB, it was compiled for the Pi at one point, but it will be slow and you will need to have an X server or Xvnc server to give xLights somewhere to display its GUI to.
When I ported it to the Pi, it was "early v3". I have no idea what it would take now to get V4 running. The main thing that could be problematic was that we flipped to OpenGL for drawing. I have no idea if the opengl stuff would even work with the Xvnc stuff. It certainly wouldn't be pleasant to use.