I found this in another thread, straight from the source:
To clarify: all current Lyrs have relay mute on turn-on and turn-off, so you can leave your headphones plugged in all the time if you'd like. However, I personally still like the extra safety of unplugging before turn-off and plugging in after the relay has engaged. It's an old habit--hard to get rid of.
All the best,
So it looks like it's safe to leave headphones plugged in all the time.