  We report a polarized Raman scattering study of the lattice dynamics of
$\beta$-Li$_2$IrO$_3$ under hydrostatic pressures up to 7.62 GPa. At ambient
pressure, $\beta$-Li$_2$IrO$_3$ exhibits the hyperhoneycomb crystal structure
and a magnetically ordered state of spin-orbit entangled Jeff = 1/2 moments
that is strongly influenced by bond-directional (Kitaev) exchange interactions.
At a critical pressure of ~ 4.1 GPa, the phonon spectrum changes abruptly
consistent with the reported structural transition into a monoclinic, dimerized
phase. A comparison to the phonon spectra obtained from density functional
calculations shows reasonable overall agreement. The calculations also indicate
that the high-pressure phase is a nonmagnetic insulator driven by the formation
of Ir-Ir dimer bonds. Our results thus indicate a strong sensitivity of the
electronic properties of $\beta$-Li$_2$IrO$_3$ to the pressure-induced
structural transition.
