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We have used resonant inelastic x-ray scattering to reveal optical magnons ina honeycomb lattice iridate $\alpha$-Li$_{2}$IrO$_{3}$. The spectrum in theenergy region 20-25 meV exhibits momentum dependence, of which energy ishighest 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 ourdata with a linear spin-wave theory based on a generic nearest-neighbor spinmodel. We find that a dominant bond-directional Kitaev interaction of order 20meV is required to explain the energy scale observed in our study. The observedexcitations are understood as stemming from optical magnon modes whoseintensity is modulated by a structure factor, resulting in the apparentmomentum dependence. We also observed diffuse magnetic scattering arising fromthe short-range magnetic correlation well above $\textit{T}_{N}$. In contrastto Na$_{2}$IrO$_{3}$, this diffuse scattering lacks the $C_3$ rotationalsymmetry of the honeycomb lattice, suggesting that the bond anisotropy is farfrom negligible in $\alpha$-Li$_{2}$IrO$_{3}$.

Optical magnons with dominant bond-directional exchange interactions in a honeycomb lattice iridate $\alpha$-Li$_{2}$IrO$_{3}$