The first modern series! With a new blue jacket, Lupin jumps right in to the 21st century.
With the decades that had passed since Part III, the series was made to appeal to new and old fans by showing the range of the series – realistic yet fantastical, hard-boiled yet comical, cool yet tongue-in-cheek. The series begins with Lupin in Italy, getting married (!) to heiress and businesswoman Rebecca Rossellini – who turns out to be a thief in her own right! But is it a real wedding or a ruse – and what other secrets is she hiding? Adventures large and small build to a wild and surreal finale.
Part 4 sets up the “modern” show structure. No more episodic 'run for as long as we can' format – now series are twenty-something episodes, alternating between one-and-done stories and installments of multi-part story arcs. The series also starts exploring what I would call "lore" rather than "continuity" – the writing carries the idea that Lupin has been active for many years, but still keeps most references vaguer and newbie-friendly.
Another interesting note about this is that Italy isn't just the setting – the show was an Italian co-production! Episodes aired first in Italy, with a different soundtrack and opening and closing. Because the Japanese version aired later, there were also minor adjustments to animation timing or frames redrawn (similar to the cleanup done for many TV animes' broadcast-to-video releases); a couple one-off episodes were released as OVAs in Japan, resulting in a slightly different episode order. And as the Italian version was localized by Toonami for the English release, all those little differences both audio and visual mean that the English and Japanese versions are released separately on both disc and streaming because they can't just change the audio track. But they're fundamentally the same episodes, telling the same story, both are fine ways to experience the story.
All that being said: an excellent entry point for Lupin. Particularly if the age of prior series is a turnoff, starting with the modern series is a fine way to get going.
I do not recommend jumping around to specific episodes of this Part. Some episodes are definitely much weaker than others, but overall its semi-serialized nature means that watching straight through is the best way to experience it.
"1st TV Anime Show Starring Lupin III in 3 Decades to Launch in Italy", Anime News Network (2014)