Did Fitzgerald perjure himself when he claimed to actually have investigated this case?
No he did not commit perjury.
Lawyers statements in court are not under oath. They never swear to tell the truth. (Many times they don't tell the truth.)
The Judge could be upset with a Lawyer who doesn't tell the truth, but most of the time, the Judge remembers when he was a Lawyer before a Judge, so he gives the lying lawyer a pass.