Let's see:
- He would never harm a child or defenseless person. - Good
- He wants to save the world from a tyrannical and thoroughly evil organization. - Undecided. Does he want to replace it with another form of government, or let everyone fend for themselves?
- He'll give the shirt off his back to a stranger if that would help them. - Good
- Staunchly loyal to his friends. - Neutral. Loyalty to one's friends doesn't swing the pendulum.
- Won't keep rewards from quests, preferring to give it back to the town or to another worthy cause. - Lawful. Thinks of the whole before the one.
- Uses torture as his primary questioning technique for prisoners. - Evil.
- Has, on several occasions, beaten someone to death with their own limbs. (This was their punishment for a crime, most likely hurting children or the defenseless.) - Evil.
- A fervent believer in eugenics, he has sterilized many useless or stupid people along his travels. - Evil. And Lawful, as he is doing that to what he sees as the benefit of society.
- Seduces women in every town he comes across, hoping to sire an army along the way (ala Ghengis Khan). - Evil. And Lawful, as he seems to be planning long-term.
So 4 Evils, 3 Lawfuls, 1 Neutral, 1 Undecided and 2 Goods. Seems Lawful Evil to me. One less Evil instace and he'd be LN. So I'll call LE (LN).