Cowboy Bebop has more fantasy to it then Lupin III has, but both deal with the same kind of characters on episodic (mis-)adventures throughout the series. Both are action-packed and have a small cast of characters.
They share mainly stylistic choices, plot patterns, dialogues and tones. They also share the trope of a group of skilled but poor "outcasts" that live adventures in many different and distant places: they spend their time between solving dangerous troubles, finding themselves in unusual situations, trying to find money and getting something for their own needs or sake. Characters also share some personality traits, like the taciturn skilled buddy or the cynical girl. There are also many references in Cowboy Bebop that are obviously tributes and homages by Shinichiro Watanabe to Lupin III.
If you dig Lupin, you'll probably dig Cowboy Bebop, and vice versa. Jazzy cool adventures with laid back badassery.
Lupin III is essentially Cowboy Bebop's cartoonier grandpa, taking itself a lot less seriously and staying purely episodic (as opposed to the overarching plot that occasionally appeared in Bebop), but having a lot in common stylistically, with a similar episodic structure, and a main cast that's uncannily similar to one another.
Cowboy Bebop seems to be spoofed off of Lupin the Third for a reason. Although they're still both dark anime, but they have two guys smoking, girls with attitude and guns at the same time, and overreacting kids. The main characters are also clever, too.
Spike is Lupin, Faye is Fujiko, Jet is Jigen, and I guess Ed is in some way, shape, or form Ishikawa. At the very least, there's some obvious inspiration here.
-They are both episodic
-They both have a cast of shady characters (Lupin and Spike as the laid back protagonist, Fujiko Mine and Faye as the femme fatale and Jigen and Jet as the mature best friend)
-They are both hand-drawn, have a 4:3 aspect ratio and were made in the 20th century
-They are both classics in their own right and they both overflow with style
-They both have excelent spin-off movies (like The Castle of Cagliostro, being the best for Lupin and Knockin' on Heaven's Door, being the only Bebop movie
Lupin and Spike are two very similar characters in the lifestyle and how to deal with things, the characters that accompany the main are very similar too, both are episodic and very influential classics in world culture