Well, as Oshun says in her bio, the one referenced above (which is well worth checking out!), we really aren't given a clue. For all we know, Lenwe simply got fed up with leadership or went off to sulk somewhere.
But if it went as I describe it here, I think it might be a good explanation for what happened subsequently, both Denethor and Thingol's friendship and the Nandor's attachment to Denethor.