The Siege of Lindos probably happened in 490 BC. Rhodes was visited by the Persians during the campaign of Darius I against Greece. The story is one of many in which during a battle in antiquity it is reported that some mythical persons appear (Epiphany), like for example in the Battle of Marathon.

According to M. Hadas based on the Lindian Chronicles inscriptions

The Rhodians gathered at the Acropolis and resisted the Persian army commanded by Datis until they had not enough water. Then they decided to hand over the city to the Persians but Athena Lindia appeared and asked them to wait as she will ask Zeus to bring water. The Rhodians asked Datis to wait for a few days until Athena will return and if she does not then they will surrender. Then unexpected it started to rain and Datis who initially did not believe the story with Athena was so impressed that he ordered the Persians to leave the island since the Rhodians as he said were protected by a goddess.

Graham Wheeler (Cambridge). Battlefield Ephiphanies in Ancient Greece: A Survey (PDF)