The library has an underused lecture theatre. Use it more!
The library could stage a series of talks from people maybe based around different sections of the library, the talk happens and then that section is focussed on so people borrow more books from it.
It could also be marketed to local community groups and businesses for comedy nights, product launches, AGMs, political meetings - all sorts of things.
The venue is already there - could Worthing Theatres help market the theatre as a new smaller more intimate venue? It would need to open until at least 10pm to make it work.