  We investigate the electronic properties of the three-dimensional
stripyhoneycomb $\gamma$-Li$_2$IrO$_3$ via relativistic density functional
theory calculations as well as exact diagonalization of finite clusters and
explore the details of the optical conductivity. Our analysis of this quantity
reveals the microscopic origin of the experimentally observed (i) optical
transitions and (ii) anisotropic behavior along the various polarization
directions. In particular we find that the optical excitations are overall
dominated by transitions between $j_\text{eff}$ = 1/2 and 3/2 states and the
weight of transitions between $j_\text{eff}$ = 1/2 states at low frequencies
can be correlated to deviations from a pure Kitaev description. We furthermore
reanalyze within this approach the electronic excitations in the known
two-dimensional honeycomb systems $\alpha$-Li$_2$IrO$_3$ and Na$_2$IrO$_3$ and
discuss the results in comparison to $\gamma$-Li$_2$IrO$_3$.
