Floyd Lawton isn't a sociopath.
He feels and thinks just like a normal person, but he's grown to be incredibly cynical and in a way, hateful. His resentment for his parents grows over the years, he blames them and himself for what happened to his brother. One of his own children died by the hands of another, but he blames himself because of his career choice. He tattoos the names of his victims including his brother and his son.
(That was until Dc was like 'nope' and erased his son from existence. I keep his son in his origin because I feel like it'd make his story more tragic, he named his son after his brother as a tribute and even that was taken away from him)
Originally Floyd wanted to be the hero, he wanted to save lives. But the way he was going to do that was killing batman, so he would always be the one in the spotlight which in my opinion, is connected to how Edward would always outshine him. But instead of that, Batman ended up putting him in prison after attempting to kill him and in his time in prison, he crafted the new and improved persona of Deadshot.
He doesn't kill for sport or enjoyment like some of the other villains on the squad, he purely does it for money. If you don't have anything to pay him, you might as well piss off because the only time he'll kill someone for enjoyment is if they've threatened him or the few people he truly cares about.
The one thing that SS truly did get wrong about deadshot is that he doesn't kill women, which is a complete lie. He has killed women, he's killed multiple women, to him the only difference is gender and nothing else, it's all about money to him, anyone with a high enough bounty is absolutely not safe from him. The only thing is, he will never touch a child, he will never harm a child, Floyd hates child abusers, he hates child molesters, he hates child killers and never wants to become one for fear of being like his father.
Waller is like a mother to him because of how cold his mother was towards him. His mother Genevieve was a cold hearted bitch who went to her own children and asked if they would kill their father. He never truly had a mother figure in his life, she watched as his father abused him and did nothing to stop it and the only reason he visits his parent's grave is to spit on them. The only true mother figure he's has is Waller and despite how much he pretends to dislike her, he does care about her.
Harley is possibly one of the few women in his life who he loves dearly, despite the fact they've tried to kill each other, that she forced him to pretend to be the Joker to get some closure with what happened to her. He loves her, that's why I always have Floyd act warmly towards her, his wife left him after learning what he did while Harley didn't give a damn. He feels like he can open himself up to her in a way and that he can trust her.
Floyd took on three gangs after learning that Zoe was living in one of the poorest parts of Star City, he became a hero to protect his daughter. He'd do anything for his children
Also Floyd is incredibly weak in his own ways, he has trouble telling the difference between Batman and his brother Edward and because of this, he doesn't have the heart to kill Batman, he can't bring himself to kill him because they're so similar in his mind. Despite his attempts to kill Batman in his career, he would never be able to go through with it. He was so destroyed by the murder of his son, that he had to be placed in Arkham because he was going insane, he couldn't handle the fact he failed to save his son.
He's not a sociopath in any way shape or form.
