We demonstrate an efficient technique to align lyotropic chromonic liquid crystals (LCLCs) using secondary sputtering lithography (SSL). Monodomains of LCLCs prepared using SSL maintained their stable alignment for days. A generalization of Berreman's theory was employed to determine the anchoring strength of LCLCs on tessellated surface patterns. The anchoring energy initially increases with the amplitude (A) of the grooves and excellent alignment of LCLCs was observed when the amplitude of the grooves is equal to half its wavelength (λ). We also note that the anchoring energy levels off above qA∼ 3 (where q = 2π/λ), which suggests that increasing qA beyond a certain value does not provide any further advantage for the alignment of LCLCs. This finding provides a useful optimization criterion for the fabrication of the patterned cells to achieve stable monodomain alignment of LCLCs. Our analysis also explains why good alignment of LCLCs has been a difficult task.