If The Immortal Bloodline does turn out to be a re-imagining of The Mystery of Mamo with The Two Lupins being the prequel, then that's great. There's enough changes for it not to be a "clone" and looking forward to it. Besides Mamo is one of the few antagonists that people really like to see and may be one of the last times seeing him.
Weirdly it does have a bit of fan service along with the rest of the series but not in an expected way as Koike referenced the manga character designs into his style and what Yuzo Aoki tried to do for Part 3 even if it didn't turn out that way...
As for fan service in general... It's really depends on the execution. Return of Pycal and Elusiveness of the Fog were both fan service bringing back a popular villain (Pycal and Kyosuke Mamo, the latter taking his manga form) but those are considered some of the weaker entries. Pycal was confusing and his character was changed. Personally I do feel like Kyosuke Mamo was one of the stronger points of the TV Special especially between himself and Lupin (and Lupin XXXIII), it's just the rest of the TV Special that lets it down. Just have a feeling that The Immortal Bloodline won't be like this and I'll imagine that the writers/staff know the complaints and the pressure to get Mamo "right" since The Mystery of Mamo is beloved.
References now and again are good. Some are neat like the Lupin vs Conan opening or spotting cameos in the background like Part 4. The opening of Missed by a Dollar was unexpected but the same time a delight. Even the likes of bring back Mister X or Fantoma for Part 2 were twists that were unexpected at the time.
I felt that Part 5 in some cases even though I liked the references really overdid the fan service and didn't have the anniversary reason to justify (like Is Lupin Still Burning?, a good example of fan service even if they just had to do THAT scene bringing it down a peg or Green vs Red where it was a case between not enough to justify the story and just right in a few scenes like Yasuo watching Castle of Cagliostro or listening to Fire Treasure, the story was the main issue with the OVA). It didn't get towards the point where it affected the plot too much outside of why did Lupin go back to Cagliostro when he could have gone elsewhere and affected some episodes more than others including important storyline episodes but was more than just a few shout outs here and there that you would expect. Even had a thought that the series might not be accessible enough for a first timer into the series just because of the references and people that appeared in it (and outside of the fanbase to have the unfair perception of having to watch the previous Parts like seasons, also gives Part 3 the stereotypical perception too). Then again there were cases that worked out okay like the assassins in the Happy Deathday Game, both a treat if you read the manga yet also tied in the plot and better than the alternative of characters that may not have had the personality that Monkey Punch gave them, they could have been generic gangsters. On the other hand the fan service also potentially caused a chance for them to not reappear again in the series especially ones that had more to do in the manga.
There's also the case where fan service is so focused that you really had to be a fan to "get it". Like The Killers in the Diner of Part 6. I'll imagine that the crossover between Lupin III fans and Ernest Hemingway fans is
very low (unlike say Detective Conan/Cat's Eye due to same animation company or City Hunter due to staff crossover) and doesn't help the dialogue is connected to the stories. I don't know if anyone who watched the episode suddenly got an interest into reading a Hemingway story. What was Mamoru Oshii thinking? (and yes, he did adapt The Killers before)
it seems Lupin has many many birthdays nowadays and feels like having an old recurring villain or jacket color is happening more frequently than anything new?
It's sadly a sign of a series of a declining interest in Japan and age plus TMS (and Sega) celebrate birthdays too. It's a way of getting interest and Lupin is getting harder to market to a younger audience especially as it doesn't fit into the modern anime mold and the closest thing is the Neighborhood Princess manga spinoff. I'm not sure if Lupin Zero did well, not well enough for an English dub and apparently why it took so long for The Two Lupins to get shown... The way things are heading, I wouldn't be surprised if remakes/reboots/re-adaptations are considered like many anime series out there e.g. Lum, One Piece (despite the main series is STILL ongoing), Ranma 1/2, the "banned" episode of Gundam into a movie and the recent Anne Shirley. The only ones that I can think of that are commercial enough for a remake outside of Mamo are Part 1 and Cagliostro as Part 2 is too long, even then they are beloved and Miyazaki probably wouldn't want anyone to do a remake of Cagliostro while he is still alive.
Saying that there are still signs of a fresh look like The First and Lupin Zero even if they also both have elements of nostalgia too...