The Lucky Duck's mother was a pookah and his father a fir darrig. After his birth he was raised exclusively by his mother, and had no contact with his father. He was brought up in isolated areas with only his mother (and two goats, implied to be his maternal grandparents) around. His mother made him promise never to wear red, the color associated with his fir darrig father.
At some point before coming to Mary's Place the Duck met Al Phee and attempted, unsuccessfully, to get information about his luck. As no mention was made of body odor it must have been earlier on Phee's personal timeline than his visit to Callahan's Place.
The Lucky Duck landed (literally) at Mary's Place its opening night (The Callahan Touch). He had been riding his motorcycle at high speeds behind Shorty Steinitz. When Shorty turned off the road, the Duck was forced to follow him. Shorty stopped quickly to avoid hitting the bar and the Duck rear-ended him. The impact catapulted him through the roof hatch of Mary's Place (losing his pants in the process) and he landed in a bar stool right in front of Tom Hauptman.
He became a regular at Mary's Place and moved to Key West with the gang. At some point afterwards he left for Ireland to attempt to help the conflict there.
The Lucky Duck lives up to his name. Due to his ancestry, his mere presence causes highly improbable events and coincidences to occur. Examples seen include flipping through all the TV channels without finding a commercial, flipping coins that usually land on their edge, and people arriving exactly when the need presents itself.