FACT: Lois had told Clark the night before he had found the cameras and microphones that she was in love with Superman.
Lois:

Why did he have to insist I be in love with his Clark persona.
Lex knew that Lois loved Superman, and that ‘Superman’ had discovered the surveillance at her apartment;
Lois:Why did Clark let us go all night under surveilance?
therefore, Lex knew that Superman had visited Lois at her apartment, at least once, but that didn’t mean that Superman loved her in return.
Maybe Lex had the roof under surveilance.
Had Lex somehow found out that she and Superman were involved, kinda, sorta, not really, the previous summer?
Yes, although I think he assumed beyond what he really knowns.
Did he do this because Clark stood between Lex and Lois, or between Lois and Superman?
The former. Although this does mean he assumes Lois is more attacked to Superman than to him.
FACT: Lex wanted Superman to die.
Lex:But it needs to be properly poetic.
Why exactly did Lex want Superman dead?
Lex is evil, need we say more?
Had Clark been right all along?
Yes.
Was Lex head of a criminal organization, or just a megalomaniac who was obsessed with Lois and anyone standing his way to that goal was toast?
Sadly it is the first.
Lois needed to find out why Lex was so fixated with her.
He is an evil man, does she really want to get close enough to him to understand how his mind works?
Did it have to do with her, as her vision had implied, or with Superman?
Why not both?
She doubted it had anything to do with her position at the Daily Planet or what he could learn about their current investigations.
At least in canon Lex agreed to the initially dinner interview with Lois to through her off the scent of his nefarious dealings with Antoineete Baines. In some ways I think that making sure Lois did not get wise to his actions was a motivation, but Lex seems to have succeeded at pointing her away for so long he no longer sees that as a threat.
Lois couldn’t picture Lex putting his entire sample in one attempt to kill Superman, so he must still have more, somewhere.
This seems a logical asusmption
What was he planning on doing with it?
make a cage?
What would Lois have to do to get Lex to reveal where the Kryptonite was or his plans…?
Convince Luthor she also wants Superman dead, and even then it would be iffy.
What was she thinking? If Lex knew that Lois loved Superman he would never willingly reveal the location of his Kryptonite vault or his plans to kill Superman.
Actually, I think she in theory could convince Lex she no longer loved SM. In practice, I think that would be too hard on multiple levels.
She would have to find another way to get Lex behind bars, and then go after his Kryptonite stash with Clark.
Shounldn't she keep Clark as far away from the stash as possible.