The first series (titled simply Lupin III, with "Part I" appended retroactively) went on the air in 1971. Lupin wears a teal-green outfit, and this series is thusly often referred to as "green jacket".
The series began under the direction of Masaaki Osumi, with a darker, more adult-oriented tone which was very uncommon (some sources say it was a first) for anime at the time. Characters were written to be relatively more complex – a major theme was "ennui", with Lupin characterized as a cynical world-weary rich ne'er-do-well staving off boredom by thrill-seeking even as the show took lurid or humorous jaunts. Special focus was given to drawing details of cars, watches, and guns to add to realism. Curiously, not many of the episodes focused on thievery, often on more general action or crime drama plots – an "outlaw Bond" spy-fi.
However, these first several episodes had low ratings, and Osumi was ordered to rework the show. He quit and was replaced by a duo: Hayao Miyazaki and Isao Takahata (who you may have heard of). They reworked the direction of the show to appeal to all ages – Lupin ditched the apathy and was now happy-go-lucky and upbeat, with a poor man's background epitomized by his little Fiat 500 (rather than the big bad Mercedes-Benz SSK).
It's not a clean split – as the change happened mid-production, most episodes are a patchwork of creatives – and as a result it can feel like two different shows at times with character designs and art style noticeably changing as well!
This series certainly shows its age – even compared to the very next installment – in production quality and soundtrack. If you can look past it – or if that retro style appeals to you – it has its own unique charms, and the characters already feel well-established. In 2021 it got a very nice remaster and brand-new English dub. It also (if unintentionally) perfectly illustrates how different writers and directors can reinterpret the same characters! It is tricky to recommend to beginners as a result of its age and quality. I at least speak for myself – who got halfway through episode one before giving up and not giving anything Lupin another look for several years!
Liner notes by Reed Nelson and essays by Daniel Thomas MacInnes, Lupin the 3rd: The Complete First Series Discotek DVD
"The Real Lupin: How the Original 'Lupin the 3rd' Anime Series Came to Be", Animation Obsessive (2024)
"Here comes Animation", a speech by Hayao Miyazaki, Nagoya Cinema Festival 1988 (translated from Japanese by Ryoko Toyama)