I'm speaking about Lucca's role in Project Kid. Lucca played no hand in making the actual FATE computer. She only contributed in making a random model board stuff which one millenium later would be expanded by Belthasar to make the Prometheus Circuit. Thus Lucca played a small role in Project Kid, but didn't actually work on FATE.
... I still don't see what you base this conclusion on. FATE was potentially created well before Project Kid was thought up. It's very doubtful that Belthasar knew of Schala's fate until Chronopolis was fully operational.
I don't see why it is you continue to argue against this: Lucca was active during FATE's creation. Lucca propagated the Prometheus circuit, which was implemented into FATE. Thus, it was a part of FATE. Now, we know she made the Prometheus circuit, which we KNOW is a part of the FATE computer complex. We do not know if she worked on more than the Prometheus circuit. However, it stands to reason that she may have worked on more than the Prometheus circuit.
There is no arguing that she created the Prometheus circuit, a part of the FATE complex.