I have no idea what his motivation is.
Basically, daddy issues.
Growing up as a son of a powerful tyrant he grew to resent power and savior figures that did nothing to save
him.
They literally make no sense. What was his endgame, really?
Destroy Superman, both as an icon and also to literally kill him.
Destroy Superman.
Was he trying to unleash unstoppable destruction on the world?
No.
Didn't care either way. Batman was a means to an end for him.
Did he want Superman and Batman dead?
Just Superman.
Or was he really just a crazy person who thought it would be funny to see heroes fight each other?
He was not crazy as in batshit crazy let's do whatever la-di-da. He had a singular goal that made sense from how the character was depicted and everything he did made sense to achieve his goal.
He progressively started losing his mind in his obsession throughout the movie, and his actions became more extreme, but they had a purpose, they were not random.
If he wanted to manipulate them into fighting each other naturally, why did he resort to kidnapping Martha and creating Doomsday?
He created Doomsday
after Batman stole the kryptonite as a contingency. He had no way of knowing if Batman will decide to fight Superman, will he save the Kryptonite for later, what he was gonna do with it, or if it will even work.
He kidnapped Martha
after Batman dared Superman to a confrontation to
make sure they fight. Again he didn't know what Batman's plan was, if he's just gonna warn him, slap superman around a bit or actually try to destroy him.
If he just wanted destruction and mayhem, why the long setup trying to turn Batman (and the world) against Superman?
Turning the world against Superman
was his plan, killing him was not enough, he had to show the world he's not a god, or a saviour, he
literally says that in the movie.
If he wanted Superman dead at all costs, why didn't he use the kryptonite himself instead of trying to make Batman his patsy?
Lex isn't a hands on guy, obviously. Especially when it comes to fighting.
He turned to the most skillfull and resourceful human being that he knew of.
What was he going to do with Doomsday when the fight was over?
He presumed he could control it(through his blood) or destroy it.
Nobody knew a nuke
wouldn't destroy them until they launched it.
He comes out of nowhere and goes in a dozen different directions. It's just nonsensical.
It's not.