Their acquisition of new releases seems to depend on the relative popularity of the new release. NYT Bestseller new releases seem to be acquired relatively quickly, for a library, but as with all/most libraries, FLP would probably score low on the Instant Gratification Chart.
You can donate money to them and (presumably) can request your favorite titles. I haven't tried this, though -- I donate to my local library because it's easier to go down and talk to them in person if the need arises.