AFAIK, the lawyer can't save themselves for a lynch.
If the lawyer was to be whacked on the same day he was to save someone, his save can only happen if the lawyer sent his request to the narrator before the Gs sent theirs. At least that's how we played it before.
Jasp, the same happened when I was the BG and I was to protect the D even while I was in jail. I sent my protection to the narrator first, then I asked the jailer to put me in prison. My protection will still be valid as it happened before.