Following Doomsday’s defeat and Superman’s death, Luthor was arrested by federal authorities and detained at Belle Reve Prison. Ultimately, the courts ruled that he was unfit to stand trial for the numerous crimes he had committed, as he was deemed to be mentally ill. Consequently, Batman arranged for him to be transferred to Arkham Asylum in order to keep an eye on him.
What makes Arkham Asylum unique is that this psychiatric hospital generally takes in all of Gotham's major criminals who have been defeated, traumatised or are obsessed with Batman. Luthor is entirely different in that not only is he not from Gotham, but from Metropolis, and furthermore, the object of his obsession is not the Dark Knight, but Superman, an alien from another planet. For the psychiatrists at this asylum, it would have been a new case.