  We report a polarized Raman scattering study of non-symmorphic topological
insulator KHgSb with hourglass-like electronic dispersion. Supported by
theoretical calculations, we show that the lattice of the previously assigned
space group $P6_3/mmc$ (No. 194) is unstable in KHgSb. While we observe one of
two calculated Raman active E$_{2g}$ phonons of space group $P6_3/mmc$ at room
temperature, an additional A$_{1g}$ peak appears at 99.5 ~cm$^{-1}$ upon
cooling below $T^*$ = 150 K, which suggests a lattice distortion. Several weak
peaks associated with two-phonon excitations emerge with this lattice
instability. We also show that the sample is very sensitive to high temperature
and high laser power, conditions under which it quickly decomposes, leading to
the formation of Sb. Our first-principles calculations indicate that space
group $P6_3mc$ (No. 186), corresponding to a vertical displacement of the Sb
atoms with respect to the Hg atoms that breaks the inversion symmetry, is lower
in energy than the presumed $P6_3/mmc$ structure and preserves the glide plane
symmetry necessary to the formation of hourglass fermions.
