Go back and watch Star Wars Episode 3. That's actually a good description of how a democracy falls to autocracy. The Republicans have been openly dreaming of a "Permanant Republican Majority" since AT LEAST Bush 43's terms in office. And they've been laying the framework since Nixon -- a newsentertainment channel that caters to Right-Winger fantasies, judges who put ideology over legality, partisan gerrymandering that concentrates Republican voters for power and dilutes Dem votes into meaninglessness, and political theories that basically advocate for the dismantling of our political systems if that will keep Democrats out of power even if they have a majority.
To answer your questions directly:
Can he do that?
Yes. He can. Anyone can.
What would need to happen to convert our system to lifetime terms?
There are a variety of ways, but they all boil down to the President doing outright illegal things under cover of a friendly Supreme Court. After all, they granted immunity to 'official acts', which we believe is cover for an autocratic takeover of the country.
What would need to happen to convert our system into a dictatorship/monarchy/whatevs?
This is just a hypothetical situation. It's July 2028. Mass incarcerations of Leftists, Immigrants, Muslims, and Minorities have begun and the country is in the throes of a civil war. Polling is reporting that Trump could lose the election, despite disenfranchising the Left's voting base through various means. Trump announces he's postponing the 2028 elections 'until things calm down, they have to get much better first before we can have a fair election." People sue. It doesn't matter what happens in the lower courts, because they'll appeal all the way up to the Supreme Court. The same 6 Conservative ideologues that said he has immunity for 'official acts' will rule that he has the right to suspend the election. And that, my friends, is how Democracy ends, with massive applause from the Alt-Right assholes that Clinton quite rightly fucking called "Deplorable".
Can Trump actually make either of those happen?
Yes. Yes, he can. The framework is already laid out. HK-65 laid it out elsewhere. Essentially, you start by shutting the Other Side out of government. You then take over all the levers of government. Then you set them so you can't lose. You might need to just waive away the safetyguards that get in your way, and some you might use your lock on government to remove 'legitimately'. If the 22nd Amendment gets in the way of a Republican dynasty, they'll have it removed.
TL;DR? Never rely on checks and balances to stop authoritarianism. In the end, the Constitution IS just a piece of paper, and will be run over by authoritarian jerks if that means power.