The cartoony factor alone doesn't make a good action movie
and while the OTT cartoony nature of "The Professional" doesn't interfere with its dark themes and extends from the performances/characterizations to the camerawork and choreography and remains consistent throughout, the cartoony elements in a film like "Lethal Weapon" seem comparatively juvenile and forced, almost as if shoehorned in to reengage the audience. It's just another action flick trope/gimmick, like an epic car chase or the heroes outrunning an explosion.
Speaking of the latter, did I mention that I recently rewatched "The Long Kiss Goodnight"? If you've never seen that one, I highly recommend it- Samuel L. Jackson's favorite of his own performances and one of the best, most entertaining bad movies of all time.