Cash Cow Franchise: Rare for an action series of its time to go to at least a tetralogy of films, all four films were box office smash hits. Each entry was among the biggest hits of its given year (4 was the only one not to finish in its year's top-ten box office, finishing 11th), and adjusting for 2019 inflation, the series averaged $262 million per entry in the United States. Even its television series was a solid ratings-grabber for FOX that was only cancelled due to being a Troubled Production and heavy Hostility on the Set between its leads.
Shane Black disliked the sequels, mainly due to how much of his script for the second film was re-written. He also said how the problem with the final version of the second movie was that they did too much comedy, and how he dislikes the other two sequels of the film because of the way they ruined Riggs' character (in his opinion, anyway).
Jeffrey Boam was unhappy that his script for Lethal Weapon 3 was largely thrown out and heavily re-written by Robert Mark Kamen. Similarly, his initial draft for Lethal Weapon 4 was unused, and his later contributions to the shooting script went uncredited due to the hectic production schedule. Boam later went on to say that both films were inferior to his original treatments.
48 Hrs. from 1982 should be considered the origin of the 1980s buddy-cop film, but the Lethal Weapon series does codify most of the tropes.
Playing Against Type: Kind of; Leo Getz, like most of Joe Pesci's characters, is a hot-headed little guy with a Hair-Trigger Temper and a filthy mouth, but where most of Pesci's well-known characters tended to back this up by being genuinely dangerous and often psychotic thugs, Leo's pretty much harmless, a bit of a Butt-Monkey and for all his bluster a pretty nice guy.
Throw It In!: Leo's rants about people who fuck you with various goods and services, (The drive-thru, the hospital, etc.) are improvised. In fact, when he goes on his rant about being fucked by the hospital in three, you can see Rene Russostart to crack up in one shot before it's cut to another. The rant he and Butters go on about cellphones in 4 is entirely unscripted, with Donner apparently just telling them to, "Bitch about cell phones for a while."