How do I deal with garen's no mana cost and regen in lane?

TLDR: how do I beat a good garen player as a mage who is squishy, requires mana to be effective, who has to deal with garen's no mana cost, relatively low cooldowns, naturally high tankiness, and insane health regen?

I played a game where I was lux vs garen mid. Sure, I can poke garen all day, but if I waste my blinding he will come at me and do the traditional q e r and im dead if I don't run with my tail between my legs by spending a large amount of mana just to place my e to slow him, w to shield myself from any damage he will inflict on me. Yes, I get it, I can just sit back and play super super safe. But basically that means he gets to be all up in my face while I have to always respect him. He has no mana cost or resource management, wins in an all in 1v1 so i have to be scared of him the entire time, he does a ton of damage if i make any mistakes at all, and even if he makes 3 mistakes it's not like i have enough damage to kill him when he has w shield+tenacity, q to break out of any slow so i dont really have enough damage to kill him, he naturally has high health and armor+magic resist from his w, and if he survives with 1 hp, he will go back to half health in less than a minute.

I've played on the other side too where I've played as garen, I could literally afk dance or taunt for 5 seconds and the lux won't be able to kill me. Takes barely any effort to play garen yet he is so forgiving and rewarding to play at least in solo queue. Garen isn't the only champion who is very strong and forgiving like this with barely much mechanical effort required, but he is one I truly hate playing against. I get he has a few weaknesses like being melee, no dash, no cc but he is still quite powerful without those things. I personally feel like he would be much more fair to play against if I got him low and he was forced to back to base rather than afk for 10-20 seconds and he is k again since he doesnt require mana and has high base health regen as well as regen passive that scales with his max health(which he gets a lot of naturally and most garens even build more health).

So I guess the purpose of this is to ask, how do I beat a good garen player as a mage who is squishy, requires mana to be effective, who has to deal with garen's no mana cost, relatively low cooldowns, naturally high tankiness, and insane health regen? I want to learn how to destroy him, beat him hard not play a scared mage the entire game playing garen's game where im scared with my heart beating fast while he is dancing because if he messes up 2 or 3 times it's not like i can kill him or punish him hard for it but if i mess up once i lose half hp or die.