  A pressure-induced collapse of magnetic ordering in $\beta$-Li$_2$IrO$_3$ at
$P_m\sim1.5- 2$ GPa has previously been interpreted as evidence for possible
emergence of spin liquid states in this hyperhoneycomb iridate, raising
prospects for experimental realizations of the Kitaev model. Based on
structural data obtained at \emph{room temperature}, this magnetic transition
is believed to originate in small lattice perturbations that preserve crystal
symmetry, and related changes in bond-directional anisotropic exchange
interactions. Here we report on the evolution of the crystal structure of
$\beta$-Li$_2$IrO$_3$ under pressure at low temperatures ($T\leq50$ K) and show
that the suppression of magnetism coincides with a change in lattice symmetry
involving Ir-Ir dimerization. The critical pressure for dimerization shifts
from 4.4(2) GPa at room temperature to $\sim1.5-2$ GPa below 50 K. While a
direct $Fddd \rightarrow C2/c$ transition is observed at room temperature, the
low temperature transitions involve new as well as coexisting dimerized phases.
Further investigation of the Ir ($L_3$/$L_2$) isotropic branching ratio in
x-ray absorption spectra indicates that the previously reported departure of
the electronic ground state from a $J_{\rm{eff}}=1/2$ state is closely related
to the onset of dimerized phases. In essence, our results suggest that the
predominant mechanism driving the collapse of magnetism in
$\beta$-Li$_2$IrO$_3$ is the pressure-induced formation of Ir$_2$ dimers in the
hyperhoneycomb network. The results further confirm the instability of the
$J_{\rm{eff}}=1/2$ moments and related non-collinear spiral magnetic ordering
against formation of dimers in the low-temperature phase of compressed
$\beta$-Li$_2$IrO$_3$.
