There are ways in which it can be appropriate to study a work of literature through the lens of a critical theory that doesn't quite fit. One can - instead of trying to make the book fit the theory, be engaged in the project of finding out just how far the book fits the theory, and why it doesn't fit any farther than it does, or to see what sort of things arise if you look at it that way, without trying to claim that this is the actual meaning. Or, one can study the theory itself, to see which books do and do not fit it.
Some studies of Tolkien roughly meet this description. Randal Helms's Freudian interpretation of The Hobbit, though he takes it more seriously than an ideal enquirer would, is essentially an exercise to see how well a Freudian interpretation fits. And Brian Attebery studies some theories of fantasy that other books fit to see why The Lord of the Rings doesn't - though he's mostly critiquing critics who try to make it fit, and then get cross at Tolkien when it doesn't.