A library need not be in LD_LIBRARY_PATH in order to be found. The point of the title is to say that libtree makes it easy to find the paths from an executable

A library need not be in LD_LIBRARY_PATH in order to be found. The point of the title is to say that libtree makes it easy to find the paths from an executable to all its direct and indirect dependencies, one of the uses of which is to help figure out what's up with missing dependencies. In reality if you're using a packaging system then you likely won't have missing dependencies, so you'd use libtree for other reasons.