The Secret of Twilight Gemini: Lara is trapped in quicksand, and will soon drown. Each of Lupin's attempts to get her out fail, he's run out of ideas, so Lara tells him to go on without her. Instead, he charges up the dune, then back again and hops with her. When she asks why, he tells her that he couldn't leave her to die alone. They both sink together.
The second TV series had the episode "The Rose and the Pistol" ("Shot Through the Heart" in English) In it, Jigen, of all people falls for a Spanish dancer. Sadly, she's just acting as part of the villain's plot to kill Jigen and Lupin. In the resulting car chase, Jigen is the one to fire the bullet that sends the bad guys' car into the ocean, killing one of the few women he ever loved.
Chapter 40 of the second manga series (English title: the Rest is Silence) is a No Dialogue Episode beginning with Lupin receiving a challenge from the samurai leader of the Nezumi Clan. A series of flashbacks show that Lupin and the samurai were childhood friends who both fell in love with a wheelchair-bound woman. Then, as young adults the samurai attacked Lupin, who appeared to be dating the woman, in a fit of jealously, which caused the accidental death of the woman. When the two meet up in present day, Lupin quickly kills the samurai, only to discover that the samurai's weapon was unloaded, implying he was a Death Seeker who wished to atone for what he did.
The episode "The Woman the Old Man Fell in Love With", where Zenigata finds someone he genuinely cares for and then she's shot and killed right in front of him when he tries to protect her. Seeing the stoic but goofy Zenigata cry in genuine grief is heartbreaking.
Elen's death at the end of Lupin III Island Of Assassins, noting that for the first time in her life she's actually felt free? Cue the water works.