Since they are statically linked, exactly what kind of dependencies could they have?..
However you can try to work it out with a several methods...
ldd <executable>
(just to be sure that your binary is not dynamically linked)strace <executable> > log.file 2&>1 && cat log.file | grep open
Where can I find a way to determine which LCL classes require which underlying APIs?
From my point of view, this purpose requires some hard work. I'd advice to try systemtap for the one.