  We calculate the susceptibility amplitude ratio near a generic higher
character Lifshitz point up to one-loop order. We employ a renormalization
group treatment with $L$ independent scaling transformations associated to the
various inequivalent subspaces in the anisotropic case in order to compute the
ratio above and below the critical temperature and demonstrate its
universality. Furthermore, the isotropic results with only one type of
competition axes have also been shown to be universal. We describe how the
simpler situations of $m$-axial Lifshitz points as well as ordinary
(noncompeting) systems can be retrieved from the present framework.
