There is no such thing as “appeal on new evidence.” And there was no reason for Giuliani to have not challenged the claim that Freeman and daughter were not committing election fraud.
After-discovered evidence, or newly discovered evidence, is an issue predominantly in criminal proceedings and may be used as the basis for a motion for a new trial. A motion for new trial is commonly thought of as an appeal of judgment. The actual mechanics is a motion for new trial. That is what is available to Giuliani when it is most advantageous to file the motion.
And there was no reason for Giuliani to have not challenged the claim that Freeman and daughter were not committing election fraud.
Just because there was no reason you understand to avoid challenging the election fraud claim, doesn't mean one doesn't exist.