  We have used resonant inelastic x-ray scattering to reveal optical magnons in
a honeycomb lattice iridate $\alpha$-Li$_{2}$IrO$_{3}$. The spectrum in the
energy region 20-25 meV exhibits momentum dependence, of which energy is
highest at the location of the magnetic Bragg peak, ($\textit{h}, \textit{k}$)
= ($\pm$0.32, 0), and lowered toward (0, 0) and ($\pm$1, 0). We compare our
data with a linear spin-wave theory based on a generic nearest-neighbor spin
model. We find that a dominant bond-directional Kitaev interaction of order 20
meV is required to explain the energy scale observed in our study. The observed
excitations are understood as stemming from optical magnon modes whose
intensity is modulated by a structure factor, resulting in the apparent
momentum dependence. We also observed diffuse magnetic scattering arising from
the short-range magnetic correlation well above $\textit{T}_{N}$. In contrast
to Na$_{2}$IrO$_{3}$, this diffuse scattering lacks the $C_3$ rotational
symmetry of the honeycomb lattice, suggesting that the bond anisotropy is far
from negligible in $\alpha$-Li$_{2}$IrO$_{3}$.
