People just see the buddy cop dynamic and see it as something fun when there's a reason why it's fun in the first place.
Lethal Weapon and its success is only seen as the movie that popularized the buddy cop formula, but I feel Shane Black was going for something much deeper that got overlooked partly due to the fact the chemistry of Gibson and Glover, which you can't blame. But Lethal Weapon is about Vietnam vets who are/were killers and are now back into regular society and they're dealing with it in different ways. They're almost like shells of their former selves. Murtagh is now a different man with a family and is now middle aged. The plot is also servicing his character as someone from his Vietnam past comes back for his help. Riggs's wife is dead and suicidal, and his loneliness and suicidal tendencies are a result of his entire past life being obsolete. There's a reason why his wife dying puts him over the edge. That was the one thing keeping his entire life from feeling useless after the war. Now her dying is the breaking of that line and it's what puts him over the edge. There's no avenue for him to use his past sharp shooting killing skills except being a cop, yet that job keeps him from actually killing himself. That's why the movie works. That's the foundation it's built on, otherwise, this movie would not have popularized the buddy movie. The very bad guys of the movie are all former Vietnam vets who are now themselves obsolete, evolve into a heroin smuggling operation because that's all they can do after their country abandoned them.
Now a lot of the tension from Riggs and Murtagh comes from the fact that Riggs is this young crazy guy who is threatening Murtagh's already worried about mortality whose life is more than half over.
The final showdown between Riggs and Mr. Joshua isn't just a macho fight, it's about these two former vets on opposing sides who could have been brothers in arms a decade earlier and have to fight it out to show that both are still good at what they've always been. Which is to kill. It has tragic subtext. Riggs and Mr. Joshua are very similar men but thrust on different sides of the law, yet the line is very blurred. This country pitted these two men against each other. Lethal Weapon is about killers of various degrees. That's why it's called Lethal Weapon. The title too is something that seems to be taken for granted. There's a meaning behind it. It's not just there only because it sounds dangerous and cool. It's an urban western first. The buddy cop thing was just a way to investigate all of that. That's why the movie works. That's the foundation it's built on, otherwise, this movie would not have popularized the buddy movie.