Is it permissible not to block the library cards of students who are late in returning books, out of leniency towards them?

The employee must fulfill the duties of his job due to the general meaning of Allah's saying: "O you who have believed, fulfill [all] contracts," and the Prophet's (peace be upon him) saying: "Muslims are bound by their conditions."

If the authority responsible for the library obliges you to penalize latecomers, then you must adhere to that. However, if you are given a choice in imposing the penalty, you may forgo it if there is a recognized benefit in doing so.