I'm not really sure but good luck man! Sounds like a misfire though, so it could be anything from a bad spark plug or wire, to a distributor, to a rotor, to a coolant tempature sensor.
Did it ever act up before? Like barely misfire, get poor gas mileage, etc?
One weird thing though, ls400's are pretty simple beasts. Most mechanics are fine working on it. Oh well, I'm sure your ls will be back on the road in no time! :)