In the scene in LW3 where Riggs and Lorna start comparing battle scars, he eventually grabs and kisses her. She quickly reciprocates. After they go to the floor, he pauses their kissing and mentions this could be a "serious ethical breach". She tells him to shut up and resumes kissing him. It looks almost like he was making sure their impending sex was consensual after his initial forward advance.
More likely it was a joke about her being in Internal Affairs.
Just how different are Riggs and Murtaugh? Their initials are reversals of each other (Martin Riggs and Roger Murtaugh).
In the first movie, it looks like the pair are on a late shift on their second night working together, because they're trying to question prostitutes for their case. It later turns out that Rianne has been kidnapped and Roger is told to meet her abductors at sunrise the next morning. Now, can you imagine that he slept at all, with both him and Trish worried sick for their daughter? Also, earlier Riggs is stated to hardly sleep on a regular basis, given how unstable the man is. Knowing that both men (and likely Rianne herself, too) are having to function after staying up for two days with barely any sleep gives a real edge to the climax, from their tortured interrogations to Riggs' final confrontation with Mr. Joshua.
It does make even more sense though, as both men were in Vietnam and Riggs in particular was a special forces operative. Having to go many hours on end without any rest is part of the job description for a commando.
Fridge Horror
Imagine being the poor police officer or ship worker who discovers Pieter after Riggs squished him.
The station psychiatrist was trying to get Riggs suspended or possibly retired because of her concerns for his mental health, thinking he was a suicide risk. But Riggs later admits to Murtaugh that while he seriously considered suicide on a regular basis, the main thing keeping him going was his sense of duty to the job. If she had gotten Riggs benched or sacked for mental health reasons, she would have taken away the one reason he still had to live, and he likely would have killed himself within a week. Her attempts to help him could very easily have ended up killing him.
