Yes, she frequents his library a lot. She doesn't have to, her personal library + her family's are more than enough, but she likes to support places that allow for the preservation and gathering of knowledge. Lucretia would also donate a lot (money and fun books, she travels a lot). Lots of things about the Dark Arts that have those paper-thin excuses like 'well, this is what the EVIL people say. And of course WE'RE not evil...'
She also leaves the Wizarding equivalent of sticky notes in the books, never puts anything away, and has a tendency to sit herself down in the middle of an aisle with a book if it's interesting enough.
And writes Dark Arts theory papers in her spare time under a pen name. But yes, she'd be in the library a loooot.