If the Universal Library contains everything, which is to say that the Library contains a true history of each and every periodic (cyclical) universe, concurrent and consecutive, then there will be the possibility of communicating across time and space.
The Universal Library is generated by an algorithm; maths applied. Any intelligence that can code an algorithm that also is slightly clever will code a Universal Library algorithm; ubiquitous. Any culture that can do that can write a letter, and that letter becomes part of the Universal Library's true history collection. The algorithm will attempt translation into its provided-set language by happenstance (English, in this case). That means that any other intelligence anywhere in space, any time, any other periodic universe, might just come across that letter.
Here is the Librarian's letter, and following that one of the many millions of replies.
Here is one of the replies, translated by the algorithm into English.