Arsène Lupin II was the son of the legendary Arsene Lupin , who took up his father's mantle as a notorious thief. Sometime during his later career, Arsene sired a son who was third in line to be named Arsene Lupin. Not much is known about the thief or his actual whereabouts, as conflicting sources claim him to be deceased but it's safe to presume that he is.
Prominently appearances in volume 5 of the manga where he escapes from prison along with several of his fellow inmates and elects to hunt down Lupin III because he believes that he is an impostor, and that his real son died years ago. A young Lupin III confronts his father and demands to know the true. Once the cops surround the building they're in, Lupin II sneaks out disguised as one with his son tagging along having seen through the disguise. Lupin II purposefully crashes the sidecar of his motorcycle into a tree, leaving his son behind as he leaves.
According to volume 2 of the manga, Lupin II was killed in a train bombing by a villain called King who sought to take over the "Lupin empire." This was also meant to kill Lupin III, but only badly wounded him. This, however, took place in a story that should be considered negative continuity as other backstory is provided that is never followed up on, namely Jigen and Lupin III having been childhood friends and Jigen having a sister (who was being held hostage by King). In the same story, Fujiko's father was a man who looked remarkably like Zenigata and went by the name Doctor. Therefore, this is an example of Monkey Punch's use of multiple choice backgrounds for the main characters, which should be taken lightly by the reader.