In Book 6 of "The Odyssey," is it pure luck that Nausicaa helps Odysseus?

it is certainly not pure luck that Nausicca helps Odysseus.  It is mostly the work of Athene combined with Nausicca's own character and Odysseus' wisdom.  First the reason that Nausicca is even present to find Odysseus by the river is because Athene suggested that she go and do the laundry as a dutiful daughter. When Odysseus emerges from the bushes he at least has the sense to cover his private parts with leaves, then when he has the chance to speak with Nausicca he refrains from throwing himself at her feet which would have probably scared her away, and speaks from a distance.  Nausicca herself shows great bravery by remaining to speak with Odysseus after all of her servants run away.  Finally, when Odysseus is given a bath and clothing, Athene enhances his appearance so he appears to be a God, so that Nausicca would want to continue to help him.