I recently re-joined my library for one reason. I can read the papers online without paying a subscription. Not many people know about this, maybe publicise it?
A book exchange, or exchanges. If someone has a chaotic life or certain medical needs they may not be able to get a borrowed book back but a book exchange where you leave a book and take a book. This could also work well for children's books.
Could you set up some form or reading club for children. I'm thinking maybe a teen doing D of E could listen to smaller children read. I know parents should be doing this but not all can and it's quite exciting for a small child to have a teen listening to them.
Offer work experience if you can, lots of schools want work experience placements. OK this doesn't bring in people directly but might encourage other teens.
A lot of schools don't have text books maybe have some GCSE / A Level / BTEC text books.
Definitely a quiet place to read / study.
Have a 'warm space' in winter. If you have AC a 'cool space' in summer.
A 'how to use the library' session, maybe in the library or maybe in local schools.
A monthly prize draw for members? Lots of businesses will give things that can be raffled / used as prizes, you could even have a business sponsor the draw.
You said it is socially mixed, is it culturally mixed? Do you want to highlight eg books written by POC? Or people with disabilities?
Could you have foreign or bilingual (if you don't already) books.