A few more to add to the list:
Fujiko's Unlucky Days (got the credits from
here) and Lupin Family Line-up OVA - Satoshi Hirayama
Italian Game - Hisao Yokobori with assistance from Haruka Inade and Asami Taguchi. Koji Morimoto had done the opening (one of the few new things for the TV Special) and since it's a different style, that counts too.
Is Lupin Still Burning? - Hisao Yokobori and Satoshi Hirayama (Makes sense for Yokobori to be involved as it looks a bit like Part 4 design wise)
Lupin Shanshei - FROGMAN
Mankatsu - Toshihiko Masuda
Lupin VIII - Shingo Araki and Michi Himeno* (Monkey Punch did do the original illustrations though)
* - I think there is at least another character designer for the series who did Episodes 3 and 5 but there are no credits at all due to its completion status. Apparently Satoshi Hirayama did the drawings for the Animage issue as well...
Part 2 does indeed have a melting pot due to its various styles, animation studios (TMS, Telecom, Oh! Production, Top Craft, Artland, Studio Korumi, Yamashita Production and others), etc. Yuzo Aoki did a few character designs in directed episodes and can easily tell. The Mystery of Mamo character design popped up partially in episodes 78 and 91, Yoshio Kabashima was credited as animator. Still finding who did the Artland episodes where the characters look like knockoffs from Cagliostro including said Count (135, 142, 152, 144 also uses a bit of this design but was not done by Artland) and Episode 62 (oval head, large eared Lupin), the latter is from an unknown outsourced studio. Part 2's credits are a bit of a mess.
Also doubt that we will know the character designer of Episode 21/22 from Part 4 since that had a completely different design for Lupin for the English/Italian versions and that had to be fixed for the Japanese version. (If there are any credits for Part 4, they seem to be from the Japanese version as TMS tend to go for basic credits for International versions up to a certain point...)
There was an artist that TMS or VAP used for many of the box arts but cannot remember the name... It looked a bit similar to Yasuo Otsuka but was not him. Ami Tomobuki (who did some animation for Part 2) had done the CD cover of Tokyo Transit, one of the last things that Yasuo Yamada had worked on.
Game wise we have:
Treasure of the Sorcerer King - Toshimitsu Kobayashi and Satoshi Hirayama
The Inheritance of Columbus is Dyed by Blood and The Greatest Battle of Minds in History (DS) - Satoshi Hirayama
Lupin is Dead, Zenigata is in Love - Satoshi Hirayama and Eisuke Sato (credited as Guest Character Design)
All of the above had some involvement with TMS and/or Telecom. Also didn't realise that Satoshi Hirayama worked on so many projects. If not character designing then some animation.
Mikio Onda and Fumiko Shīya did the drawings for Hong Kong no Mashu, there is no character designer credited as to be expected for an early game but some of the artwork does look "traced" from Part 2. There are no character designer credits for Sage of the Pyramid (only Monkey Punch is credited but obviously not his style) but does have a strange "Jacket Design" credit Ryo Fukushima, the same for Master File and Chronicles. The rest either don't have any credits at all or not easy to get them...
Then there are the other manga artists since the OP did say about people drawing the gang:
Eiichi Saito (Lupin VIII)
Shusay (Lupin S)
Masatsuki Yamakami (Lupin Y)
Yukio Miyama (Lupin M)
Naoya Hayakawa (Lupin H, Lupin Italiano)
togekinoko (Lupin T and an eye catch for Part 6)
Tamio Baba (Lupin B)
Okada Tai (Zenigata)
Kazumi Hoshi (Goemon)
Izo Suzuki (Fujiko Mine Company)
Keyaki Uchiuchi (Neighbor World Princess)
I think a few of these also did covers for Lupin III: Official Magazine as well. Some other mangaka had done Lupin drawings such as Gosho Aoyama and Tsukasa Hojo but mainly for promotion.