Hi @Julien,
I am wondering how to do this in an easy way for quite a while (and I do not yet have that easy solution).
Have a look at http://in-thread.sonic-pi.net/t/smoothly-fading-samples-and-synths/528; towards the end @robin.newman proposes a smart solution, though it is not as concise as I would wish it to be for a live coding situation.
In case you want to fade the whole buffer (fade the whole track), you can always use something like:
set_mixer_control! amp: 0, amp_slide: 16
For fading single live_loops I currently also use the approach @chris.krakou mentions (of course you can control any parameter with it, such as a low pass filter); the problem with that is, that you will have a stepwise fade (in the above example each fading step takes 0.25 beats).
If your live_loop has a runtime of e. g. 8 beats you can apply control (see some ideas of how to do that in the mentioned thread).