my LC does similar, although not to your extremes. it doesnt stall, but sounds like it will but it then recovers itself. It has done this since i got it last year - the only thing that helps is the cleaning of the TB and the TBA. Sorted it for a while, now its back again.
its always just after a journey, when i pull up at lights or junction or home, it idles for a few seconds, revs drop then it recovers. Does it once or twice but then idles fine while i let her cool down before switching off.