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 Schrodinger 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.
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