A pressure-induced collapse of magnetic ordering in $beta$-Li$_2$IrO$_3$ at $P_msim1.5- 2$ 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 ($Tleq50$ 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$_3$.
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