Hey, I might lose my job if I save your life
Lawyers are required to defend their clients, regardless of whether they think they are guilty or not. Personally, I think this is bollix. Your lawyer knows your case better than anyone else, and if you can't convince him, what chance do you have with a jury? If you can't find a single person to represent you, who believes you're innocent, then you're probably guilty.
What do you think of the attorney/client privilege? That's where your lawyer can't reveal anything you say to him in confidence; like doctors and priests.
There's that old chestnut of the priest who hears a murderer's confession and can't tell anyone; what does he do? Traditionally, nothing.
But here's the case of an innocent man kept in prison for 26 years for a crime he didn't commit, even though the truth was known to lawyers. They claimed that they were legally bound to keep their own client's (the guilty one) revelations a secret.
Dale Coventry and Jamie Kunz (actually, I think they're both Kunz) claimed to have a suffered sleepless nights (in comfortable beds) over their decision to keep quiet. But when Alton Logan (the accused) didn't get the death penalty, just life in prison, they felt they didn't really need to act on his behalf.
Gee, thanks. They stopped short of killing the guy.
They felt they couldn't come forward because of the Illinois State Legal Code of Ethics, a breach of which might get them (gasp!) disbarred. Not only that, they had 'an obligation to protect their client,' the self-confessed murderer.