Sexually illicit? That is quite different from sexually explicit, which might be along the lines Doc John suggested.

My guess is the library has policy already to deal with this. Even if the library doesn't require parental authorization, perhaps parental notification is allowed. In our library system, parents have access to information about what items the child is borrowing (they can look it up online but it isn't "pushed" at them) and are allowed to pick up "holds" for the child at the library. If a book is overdue, the parent is notified, and the title of the book is included in the message (title is always included no matter if the patron is child or adult). When a minor turns 18, the policy changes and the library requires written consent between adults to have access in various ways to each others information or to be allowed to pick up each other's books. In my home, this situation probably wouldn't have happened because we have to drive to our local library and 11 year old could not get there on his own, so I would be there in person when my child was checking out books. It could be that this boy's parents know what their 11 year old is checking out and are OK with it.

Good question, Debbie! I am curious about other library lending policies besides my own local system.

(I think my library does not have pornography in their collection--as a test, I checked the system catalog for Playboy and they do not subscribe. So, in a way, they are controlling access to certain types of material by not having those materials.)