When Lupin reunites with Riko, his daughter. He's a bit unsure of himself with how to interact with her, but he does show that he cares about her by regretting not seeing her childhood since he died before she was born.
The entirety of Lupin reuniting with his old gang, even when Goemon and Fujiko refuse to join him in a final heist, the only exception being Jigen who he's getting one last favor from.
Zenigata's short encounter with little Shirou is absolutely adorable, even more when the kid is inspired to become a cop by it - even before the fire and trauma, Shirou wanted to become an Ally of Justice.
Lupin saving Sakura and referring to her as a princess, leading to her regaining hope after a year of being hopeless. All a direct callback from The Castle of Cagliostro.
Kariya being happy and content with his life after Assassin/Lupin saves Sakura and he helps the thief kill Archer, thus giving Tokiomi one final FU for taking his wife and children for granted. He even calmly accepts his death at the hands of the Owls.
Jigen and Natalia's interactions with each other in Jigen's flashbacks, and despite Natalia betraying Jigen they still do care for each other deep down.