
Lawrence is the antagonist, the evil brother of the unusual MC and he has typical behaviour and attribute of a ML in any Asian dramas or novels.
It is not that hard to read the summary and the chapters of "The Villainess Lives Twice!"
Izekiel is not exactly the tyrant king or the main ML. It's Claude!

You're right that Claude holds some typical tyrant characteristics. He's cold-hearted and only puts up with those he chooses to keep around. However, he's not exactly a tyrant. At least not to his people. He runs his country well, the people love him. He doesn't go around causing destruction just because he has the power to do so. In fact he mostly minds his business and is a workaholic.
Did he kill Athy in the past? Yes. But let's face it there was a lot of circumstances that suck that led up to it bc Claude is an idiot who was in pain from losing Diana. That's his fault entirely but we see that he becomes a doting father under completely different circumstances. Comparing him to Lawrence isn't correct bc Lawrence is abusive, uses ppl as you said and runs his country to ruin. Nobody likes the guy, except his mom.

It does not excuse his heinous behaviour towards his helpless poor biological daughter.
And I find very absurd and dumb that he is now currently suffering under amnesia which leads him forgetting his precious time with the MC and trying to kill her again without any hesitation!!! (What was the author thinking?)
What pisses me off is the very fact the his close allies don't do much to stop him or have the guts to protect Athy! Are they fucking dumbasses or foolish accomplices?!
Considering his fucked up mental state there is no way he would keep the country running on the long term, if it wasn't for the love he was given by the kind women in his life!
I prefer ML fathers from "I Was Born As The Demon Lord's Daughter" AND "The Archmage's Daughter". And the Monster Duchess :)
These parents didn't have to be wear down, sucked up or kissed by the female MC to love her. On the contrary they took the initiative to learn to take care of a child.
Unlike egomanic Claude they did not abuse their children!
Yes, the Demonlord blamed the MC as a newborn baby for the death of his beloved wife and had the urge to kill her but he stopped on time and realized his mistake! To redeem himself he decided become a caring competent father!
Did Claude ever apologize to Athy for almost drowning her????
And because he is such a desired heartthrob/fuckboy with a sad past he gets always a pass.
I hope you understand my disapproval of royal male characters in power like him.

He is under amnesia because he protected his daughter though?? He literally rushed in and gave up his own mana and didn't think twice about the consequences so he could save Athy. Also, people forget but Claude literally froze his heart and erased his memories after Diana's death causing him to initially be cold towards Athy but we see that clearly not last long. He neglected her, but that's rlly the only abuse he inflicted on her. After he loses his memories and has absolutely no idea who she is, sure, he tries to harm her, but again, to him she's a stranger and he blames her for his condition and the fact she has his mana. He doesn't understand the situation. He's confused. All he knows is a little girl has his mana and he's extremely unwell.
Other than that he's not a bad dad. The manhwa does a poor portrayal of how he really is with Athy. He's much more affectionate in the novel and truly cares for her. He's not a perfect character and he clumsily learned to be a dad after he went through lots in life, some might say that doesn't excuse it but this is a new reality where he's not the person he was before. Not everyone needs the same type of affection and show to tell someone loves them. I believe Athy and Claude have their own relationship understanding and they're happy that way.
Everyone has their preferences and it's totally okay if you don't like him, I'm not forcing you to nor do I plan to change your mind. But these are some facts and thoughts to keep in mind. I'm not fond of Royals in power who get passes either :/

I believe you that the novel version is much more detailed. There are adaptations that leaves out important informations, inner monologues and moments.
I respect your arguments. It is just soap opera logic that bothers me:
Amnesia, magical spells to freeze your heart/feelings away, everyone is connected through dramatic background, secret revealations, inhumane ML is untouchable and so on...
That reality where Claude becomes a better person only exits because MC Host is doing all the hard emotional labor and is too lenient towards that fuckboy.
Melissa from "Beware of the Villainess" or Su Lüxia from "Cheating Men Must Die" would have beat the shit out him. When you read these webtoons, you will see why these bitches won't fall or sympathize with Claude at all.
But as you said everyone has its preferences and that's ok.
One of the reason why I am not a fan of Claude and his people is because they remind a me of my messy family dynamic. In my younger years I came to the realization after suffering long enough in that enviroment:
"Wait a minute? Why the hell do I have to fight and suffer for family members approval who are miserable hypocritical assholes? Why is their toxic way of showing their love towards me so acceptable? Do I really need to like/love them just because they are popular and respected in some circles? Do I have to forgive every mistakes they did just because of circumstances? Is my only option to stay with a family that keeps making unhappy so I can survive? No way in Hell! Screw them!
And that is why I am more fond of stories where ML archetypes like Claude gets accountable and suffer real lasting consequences for their foolish actions!
I recommend you to read the "The Villainess Lives Twice!"
In other Asian novels the saint/heroine/false villainess would usually heal or make the typical cruel sadistic narcisstic immature goodlooking alphahole a better man through naive unconditional love no matter how bad he is... YIKES
But in this story the author is not sugarcoding or lenient towards a "prince" called Lawrence and this time the characters around him don't take his bullshits! It is made very clear that this shiny shithole only made it to the top because he had competent support!
If you ve read "The Abandoned Empress", "Daughter of the Emperor", "I Became a Maid in a TL Novel" or other stories that involves an abusive (op) bloody tyrant ML character that the suporting or side characters are so stupidly loyal to him that they have any excuse for his shitty behaviour like almost killing the MC in cold blood or the way he can easily harm and dispose anyone who annoys him.