  ${\beta}$-LiGaO$_2$ with an orthorhombic wurtzite-derived structure is a
candidate ultrawide direct-bandgap semiconductor. In this work, using the
non-adiabatic Allen-Heine-Cardona approach, we investigate the bandgap
renormalization arising from electron-phonon coupling. We find a sizable
zero-point motion correction of -0.362 eV to the gap at ${\Gamma}$, which is
dominated by the contributions of long-wavelength longitudinal optical phonons.
The bandgap of ${\beta}$-LiGaO$_2$ decreases monotonically with increasing
temperature. We investigate the optical spectra by comparing the model
Bethe-Salpether equation method with the independent-particle approximation.
The calculated optical spectra including electron-hole interactions exhibit
strong excitonic effects, in qualitative agreement with experiment. The
contributing interband transitions and the binding energy for the excitonic
states are analyzed.
