I don't recall ever seeing or reading about The Joker defeating the Justice League. At best, in some continuities, he succeeds in corrupting a hero like Superman (as seen in the game Injustice), but it those wins usually leads to his death (in Injustice, Superman kills the Joker).
Currently in the comics, Lex Luthor is a Martian/Human hybrid in order to become an Apex predator. In this form, Luthor has proven to be a powerful villain against the League.
Luthor, in his traditional form, and The Joker would have difficulty beating the Avengers. Luthor's key trait, his high level intellect, is rivaled by several of the Avengers (Iron Man, Ant-Man, Black Panther). The Avengers have experience fighting evil geniuses and corrupt businessmen. Luthor would be easy to fight.
The Joker is unpredictable, but he is still powerless. Again, most of the Avengers have fought against mentally insane villains before, so The Joker is not much of a threat.