This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Lethal Weapon
Riggs' suicide attempt in the first film.
Roger's Heroic B.S.O.D. in the third film after he found out one of the people shooting at him that he killed, was not only a teenager, but his son's best friend.
The scene at Murtaugh's boat. After Rianne visits Riggs telling him her father hasn't come home the past few days, Riggs decides to go see his partner at his boat, only to find his grizzled partner in a drunken stupor. Riggs tries to snap Murtaugh out of his depression saying that his family has been worried about him and that if Murtaugh didn't kill Daryl, both he and Riggs would be killed along with many others, but Murtaugh still won't listen. He further laments how he killed a youngling and that Riggs has no problem killing people since he himself has his own kill count and that he has ice in his veins, but then Riggs retorts by calling Murtaugh a selfish bastard. Riggs then brings up that whatever happens to Murtaugh happens to Riggs and that when Murtaugh retires, it'll be the end of not only Murtaugh's career, but of their partnership, to which Murtaugh replies it's not his problem. Riggs then replies that Murtaugh is the only family he has and he's wondering about what he's going to do without him. Murtaugh and Riggs go back and forth each other until Murtaugh starts breaking down, realizing he doesn't know what he's saying or thinking anymore. Murtaugh then apologizes and tells Riggs that he didn't realize that him retiring would screw him up.
From near the end of the fourth movie - "Riggs? RIIIIIGGS?"