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The article is concerned with the assessment of a cumulant lattice Boltzmann method in wall‐bounded, separated turbulent shear flows. The approach is of interest for its resolution‐spanning success in turbulent channel flows without using a specific turbulence treatment. The assessment focuses upon the flow over a periodic hill, which offers a rich basis of numerical and experimental data, for Reynolds numbers within 700≤Re≤37,000. The analysis involves the mean flow field, second moments and their invariants, as well as spectral data obtained for a wide range of resolutions with 2≲Δxi+≲100. With the emphasis on a recently published parameterized cumulant collision operator, the universality of the value assigned to a stability preserving regularization parameter is assessed. Reported results guide resolution‐dependent optimized values and indicate a required minimum resolution of Δxi+≈30. Analog to the findings for attached turbulent shear flows, the approach appears to adequately resolve complex turbulent flows without the need for ad hoc modeling for a range of scale resolving resolutions.