I disagree, a lot of Lupin's best stuff was from those 2000s specials. There were a couple I found weaker, but many I really liked. Compared to various episodes of part 2, a lot of these compare very favorably. And overall a more solid selection of specials than the 90s ones or ones from this decade.
2000 - Missed by a Dollar - this is awesome.
2001 - Alcatraz Connection - this is awesome.
2002 - Episode 0: The First Contact - very awesome, one of the best specials ever.
2003 - "Operation: Return the Treasure - this rocks.
2004 - Stolen Lupin - This also rocks.
2005 - An Angel's Tactics - Very cool, one of my favs.
2006 - Seven Days Rhapsody" - another one of my favs
2007 - Elusiveness of the Fog - Not a fan of this one, first boring one of the lot for me.
2008 - Sweet Lost Night - Possibly the best Lupin special ever.
2009 - Lupin III vs. Detective Conan" - Surprisingly entertaining, never watched Conan.
2010 - The Last Job - This was okay, had it's moments, but not one of my favs.
I reviewed most of those on myanimelist, for the record. https://myanimelist.net/profile/Psycho_Kenshin/reviews
But since the OP is about art style, I'll just say to me that's some of the best Lupin has looked aesthetically. Compared to other anime it's surely not generic, and for me it's a better style than the one Fujiko or the more recent series had.