Can I lecture on a subject that references (as required reading) a book that all were required to read? I am not reproducing any portions of the text, and assume they all legally procured the work.
Yes, you can require your students to read a book for a class. Where the students get the book is then their problem, and as long as you don't provide them with pirated copies, the origin of their copies needs not be your concern.
The only concern many of us have these days is that many books are expensive. This may not be true for a softcover copy of some classical literature, if that happens to be your area of teaching, but it is an issue if your area is some advanced topic in the sciences where many textbooks can run at $100 or over. I have generally avoided requiring my students to have a particular textbook for these reasons -- going to college is expensive enough these days.
Copyright is about copying. You aren't doing that. In fact most university courses have required text books, but instructors don't check to see that the students have receipts for purchase. You are fine, actually. The assumption you make is entirely typical.
If students pirate books in some way, that is on them, as long as you don't suggest or encourage it.
But lectures based on the material of others is fine. Universal, actually.