Upvote:3
I am afraid this question cannot be answered, because the fate of the library is not known. It is unlikely that it still existed at the time of Theon.
For the first time it was burned by Caesar in 48 BC. It is not known how much remained after this first burning and whether it continued to function as a library. Another possibility is that it (or what remained of it) was destroyed by Aurelian (200s AD). In 391 AD pagan worship was abolished by Theodosius, and pagan temples were closed. The library was a part of the temple of Serapis, so certainly it did not exist as a library after that time. This was during Theon's lifetime. He was 12 years old.