In his fourth birthday vignette Malleus explains that he had multiple tutors for things like history and manners, but he was so much more powerful than his magic tutors that as a young child he would throw temper tantrums out of frustration and drive them away.
Malleus also mentions an unnamed “mentor” who would scold him most severely every time he drove off one of those tutors, and it is possible that that mentor was Lilia.
Malleus mentions Lilia cutting his hair, having him memorize a book about survival, singing to him at night and teaching him how to play string instruments, while Lilia himself says that he trained Malleus (in addition to Silver and Sebek), so it seems that multiple people including Lilia have been involved in Malleus’ education.
Twisted Wonderland Reference Note 