What if he isn't lying? Lying, to me, implies he is doing it intentionally knowing it's wrong. I believe he believes it. That's the thing about conspiracy theories. You're allowed to have a different opinion. You're allowed to disagree with the main view.
He has admitted to believing that the shooting happened and that children did die at Sandy Hook.
It's no different than if Trump saw posts here from liberals and then sued them all for slander.
It is different because Trump is a public figure, he put himself in the spotlight, so the bar is higher than for a private person who is highlighted by a tragedy not of their own making. Trump would have to prove that it was slander, untrue and known to be untrue, and that he was harmed by it. These parents who sued were defamed, exposed to public ridicule, accused of being "crisis actors" on a popular platform after their child was murdered. Jones played video clips edited to deceive over and over.
I mean, where do we cross the line on what is free speech? Are you the moral authority who gets to tell people what they can or can't believe?
When speech is untrue, known to be untrue, harmful and defamatory the line is crossed. The reason the Jan 6 hearings are revelatory is that so many people have testified that Trump was told by trusted people, in the position to know, that he lost the election fairly, but he continued to claim otherwise. If, despite all the evidence, Trump really and truly believed he won then he was and is delusional which calls for the 25 Amendment.
People often say free speech has consequences, but if that's the case, then there's no such thing as free speech.
You are right that free speech is not absolute (few things are). You are not allowed to wantonly harass and defame people, especially non-public people.
Should people be punished for their opinions or beliefs?
That's a different question. Short answer: no. However, you can be punished for actions based on beliefs. See
Sovereign Citizens (pdf) for example.
You'd have to prove with evidence that Alex Jones caused harm by intentionally lying.
He didn't show up in court to defend himself, so he lost that case by default. However, during the trial to determine damages, he was caught and called out for lying under oath more than once by the judge (not in hearing of the jury, but on camera).