During the Dance of the Dragons, Lucerys Velaryon was sent by his mother Rhaenyra Targaryen, to gain support from Borros Baratheon, who had declared for neither faction. However, Aemond Targaryen and Lucerys had arrive consecutively at Storm's End. However, Borros had already came to the conclusion that Rhaenyra was inferior to him, and banished Lucerys from the castle.
However, Aemond wanted blood. On his way back to Dragonstone, Lucerys was caught in a storm above the fortress, and his young dragon Arrax could not take it. Aemond then rose to Lucerys' elevation on Vhagar, who was five times the size of Arrax. Vhagar bit into Arrax's neck so hard that she decapitated him. Arrax's lifeless body fell, with Lucerys on it, and he drowned in Shipbreaker Bay.
Rhaenyra was unsure whether to end the civil war right there, but Daemon Targaryen said that Lucerys would be avenged with the death of Aegon II Targaryen's eldest son Jaehaerys Targaryen (son of Aegon II).
In the books
Lucerys flew to Storm's End, arriving before a gathering storm. He found PrinceAemond and his dragon Vhagar already present. Aemond tried to goad Lucerys into a fight, insulting him, calling him a Strong bastard, but Lucerys, sworn not to fight, refused him. He delivered his message to Lord Borros Baratheon, but was refused and told to leave.
Borros prevented Aemond from attacking his cousin in the castle, but did allow for the prince to follow him. Mounted on his dragon, Aemond caught up with Lucerys during a raging storm. The fight between the two dragons did not last long. Vhagar, being five times bigger, had the advantage, and Arrax fell broken. His head and neck washed ashore three days later, along with the corpse of Lucerys.