The claim that decades of culture and advancement were destroyed is usually considered exaggerated or completely untrue, as far as I've seen. If that is the case, then what was lost?
A similar question https://www.reddit.com/r/AskHistorians/comments/5t6op5/facts_about_the_library_of_alexandria/ddkr2h6/ has been answered by /u/XenophonTheAthenian.
TL;DR: there is no proof or even indication that anything important was lost with the Library.