Not only does Lilia not call Silver his son during the Spectral Soiree event of 2021, but his phrasing insinuates that he comes close and then changes his mind:
Original Lilia: What an admirable……
EN Lilia: What a model son you are.
Lilia’s words trail away before he finishes speaking, but he might have just barely stopped himself from saying, “an admirable son.”
That seems to be what EN’s interpretation was: the word “son” was even added outright to the English-language game, but Lilia did not actually say it.
While Lilia will refer to Silver as his “pupil” and, in a flashback, as “the child I look after,” he did not refer to Silver as his son until 2026, in Book 7.5 of the main story when Silver was officially adopted.
Lilia: …Silver. I may have raised you from childhood, but legally, I was simply your guardian. Yet you expressed a wish to be my true son. And Malleus and Sebek supported it. Here.
Silver: What’s this form…?
Lilia: A formal adoption application I sent for, from Briar Valley’s Ministry of Justice. I’ve signed my name to it. Once you add yours, we’ll be legally recognized as father and son. It isn’t as if a mere sheet of paper will change things for us very much, but…I am glad to get to call you my son.
Twisted Wonderland Reference Note 