IDM uses parallel downloads (it downloads multiple segments of the file at once) in order to maximize your download speed. Livestreamer does not do this by default and it may not be possible for some streams (depends if the server allows it).
To imitate this function in Livestreamer, provided you're watching an HDS or HLS stream, look into the options hls-segment-threads and hds-segment-threads. (
http://docs.livestreamer.io/cli.html under "stream transport options") I haven't used them myself, but the documentation makes it sound like it would download similarly to IDM. I think IDM uses 4 or 8 parallel streams at once, so you could try setting it to 4 and see if that improves the speed.