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Ensembles of two-level systems interacting with a single-mode electromagnetic field are increasingly being used for the development of quantum information processors and mesoscopic quantum devices. These systems are characterized by a set of energy-level hybridizations, split by Lamb shifts, that occur when the ensemble and field mode interact coherently with high cooperativity. For high dimensions simulating system dynamics while including the complete set of Lamb shifts is generally intractable. We present a compact description of Lamb shift statistics and behavior across all collective angular momentum and excitation subspaces of the ensemble without resorting to overly restrictive approximations of the state space. We also calculate the averaged effective Lamb shift weighted over the degeneracies of these subspaces to connect our results to experiments. [ABSTRACT FROM AUTHOR]