  Two atoms in an optical lattice may be made to interact strongly at higher
partial waves near a Feshbach resonance. These atoms, under appropriate
constraints, could be bosonic or fermionic. The universal $l=2$ energy spectrum
for such a system, with a caveat, is presented in this paper, and checked with
the spectrum obtained by direct numerical integration of the Schr\"odinger
equation. The results reported here extend those of Yip for p-wave resonance
(Phys. Rev. A {\bf 78}, 013612 (2008)), while exploring the limitations of a
universal expression for the spectrum for the higher partial waves.
