For me, it works really well to get me to speak more freely and openly. It was important at the start (and it still is) that I knew that I could go back to sitting up at any time, though; I lie down for my own benefit, not for T's. He first suggested it after a few months, for the same reason that your T suggested it, but then I thought it would be too weird. Several months later (almost exactly a year ago, now) I asked to do it, because I was still having trouble opening up after more than a year. Here's my experience of the first few times lying down:
http://forums.psychcentral.com/psych...reclining.html
I sometimes return to sitting up, for one or a few sessions, but mostly I lie down, still. T periodically asks me about my thoughts around sitting vs lying. He does sometimes feel more distant, especially when he is silent and doesn't respond to what I say, and I do sometimes wish I could see him, but on the whole it has worked wonders for my ability to talk.