Līber, free. For luber, as we find Libet and Lubet. Libens and Lubens.
Liber (with short i), the inward bark or rind of a tree. And, as this was used for writing on, liber came to signify a book, volume. For leber, which Quintilian states was the ancient word.
(from An etymological dictionary of the Latin language. By Rev. F.E.J.Valpy, A.M.)
Those are different roots.