We investigated the effect of application of hydrostatic pressure on the charge-density wave (CDW) state in Lu(Pt$_{1-x}$Pd$_x$)$_2$In by electrical-resistivity measurements. In Lu(Pt$_{0.7}$Pd$_{0.3}$)$_{2}$In we find an increase of the CDW transition temperature upon application of pressure, which is not expected based on simple volume arguments, but in line with results of a theoretical work by Kim et al. [Phys. Rev. Lett. 125, 157001 (2020).]. Combining experimental and theoretical results suggests the existence of a CDW quantum critical point in stoichiometric LuPd$_2$In around $papprox20$ GPa.
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