That's explained in the first series. Lupin the Third is the grandson of the original Arsene Lupin, and son of Lupin the Second. Zenigata is also the grandson of the french detective Zenigata, that moved to Japan after Lupin the Third's father. All this, must I add, didn't fall favorably on the original copyright holders of Arsene Lupin. A interesting fact is that the international version of Lupin (playing in Portugal), has the original openings, but not the original music (the one with the "Lupin da thiird" refrain), and the title's been (crappily) replaced with a "Cliff Hanger" logo, like the version that showed on the states years ago.
EDIT : I'm still seeing Scrapped Princess and Last Exile. Heluva good shows, they are.
EDIT : I'm still seeing Scrapped Princess and Last Exile. Heluva good shows, they are.