Not only does Lilia not call Silver his son, but his phrasing insinuates that he comes close and then changes his mind:
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 has yet to say “son” as of this writing, though Silver himself has said it.
Twisted Wonderland Reference Note 