Shahpor,
You have one of theses fancy Mk 4s so it may not be the same but there was a thread about a startup noise on Mk 3s. From memory it was thought to be due to no oil somewhere high up on the engine where pressure holds a mechanism in position. Lack of pressure and it isn't held tightly and rattles a bit. VVT perhaps? As soon as the oil pressure builds up the rattles stop. You say doesn't happen very time the engine is started but only when it has stood overnight. If it is the same Britprus has a cunning fix but it's not one Lexus would do for you. He will advise.
John