Lets start with the actual 7 digit model number from the model number tag since there are 17 different models of the IS500Z. And then also get the model number info off of the valve cover.
I suspect the run and or start issue is related to the battery/charging system. Also if it is the engine I am thinking most likely has a leaking sump gasket. And 542 hours with proper care should be about the half life of that engine.