Should i breakup or not?

Long-term relationship, he takes care of me like a kid whether we are out or in our private space Tells me that he loves me like 10 times a day. Emotionally available, protective,highly respectful and a nice guy.Looks Fine. But..he lies on things which i can stop talking to him or maybe just block him because i have got solid boundaries. And he has a terrible past, him being in a fwb and pron btw i caught him while being in a long distance initially. But i was really naive that i didn’t actually know what happens in pron ,i blocked him forever. But he came back running behind me for a year almost,until i gave him a chance. And this is constant he makes me talk to him by hook or crook He literally keeps texting everywhere day nd night until i start talking to him. He says he is obsessed with me and doesn’t even like to see around. But he still lies, I’ve checked his phone but everytime i found lies Not to an opposite gender but like going to watch movies ,outing with friends without letting me know. I know it’s a red flag but i feel stuck bcz i really want him to love me like he does except those mischiefs. But at the same time reality hits and tells me to never forget his lies and carelessness despite of knowing how it would make me feel. But then again he will come back running anyhow. What to do??