This is very normal under American law. If you are legally insane, you cannot be executed. If the lawyer believes what he is saying, it is fine. A lawyer has a duty to advocate for his client. Sometimes this can even mean doing things against the client’s wishes, though this is tricky issue and rarely occurs. A client can always fire his attorney.
Under American law, to decide whether someone should be sentenced to death, the jury considers both aggravating (factors that make the death penalty appropriate) and mitigating circumstances (factors that would make it not appropriate). One mitigating factor is mental health. So even if someone is not legally insane, if they have serious mental health problems (“defendant’s capacity to appreciate the wrongfulness of the defendant’s conduct or to conform conduct to the requirements of law was significantly impaired”), that could be something the jury could consider in deciding whether to impose the death penalty. The jury should hear all the relevant information on both sides and then make its decision. It’s fine if the attorney argues, look, given all the information I’ve shown you, you should conclude that based on his mental health problems, he doesn’t deserve the death penalty.
If he’s actually innocent, may he be speedily released.