  The aim of this paper is to show that within the open-system framework the
sum-over-modes approach \'a la Casimir leads to the Lifshitz formula for the
Casimir free energy. A general result applicable to arbitrary geometries is
obtained through the use of Ford, Lewis, & O'Connell's remarkable formula.
Additionally, we address the possibility for obtaining the Casimir energy as a
sum over complex "modes". We show in this case that the standard sum-over-modes
formula must be suitably generalized to avert unphysical complex energies.
Finally, we apply our results to several standard examples.
