well well well, .... this was aN annoying problem too on my Mk3 a couple of years back .... scared me rigid at the time but as you say, stop the car somewhere safe, turn it all of and BINGO ..... it all starts up again ok and lasts until .... well, the next time.
It hasn't happened to me for absolutely ages now but when it does I know the simple solution.
My indy reckoned it was probably the ignition barrel too and if it happens again I might get him to sort out the problem.
It's not just Ls400s, it happens to VWs too he tells me.
Maybe it's just age related and not using the car enough .............. maybe the Ls is telling us not to take it's apparent brilliantness for granted eh !
Malc