Lee Everett is slowly losing all control of his life. First the betrayal of his wife, then the zombie-apocalypse and all the stress that it brings.. Then the loss of his arm and his imminent death. Lee feels governed by the misery of his surroundings, he is in control of nothing. And so he seeks control in the only way that he knows how... Imperfect tragic Love.
Little is known about Lee Everett, except for that he has a stormy past. He comes from a broken home where the only thing that was taught to him was violence. His parents brought him up through abuse, they displayed their love to him through scoldings and beatings, but they also punished him through scoldings and beatings. This left him a broken and conflicted soul, always wishing to do what is right because all he wants is to be loved. But also prone to anger and violent fits when he feels pressured and misunderstood.
This is why there are options in the game for doing such terrible things as Lee does. Killing other human beings just because you feel like it. You wouldn't be capable of the things that Lee Everett is capable of unless you had experienced the terrible things that he has.
The terrible loneliness caused by the zombie apocalypse causes Lee Everett to evolve feelings for this small girl that has become like his daughter. He finds himself feeling something that he never has before. In a way, this could happen to all of us. If we just find ourselves in a place completely broken down and desperate enough for love we will do anything we can to attain it. In one last desperate attempt to experience love and affection, he puts his hands on her like he never has before.