  We study the pairing instability of a two-dimensional metallic system induced
by Ising-nematic quantum fluctuations in the presence of an unavoidable
relevant coupling of the nematic order parameter to the elastic modes (acoustic
phonons) of the lattice. We find that this nematoelastic coupling
$\lambda_\mathrm{latt}$ leads to a decrease of both the superconducting (SC)
critical temperature $T_c$ and the gap function $\Delta$, regardless of the gap
symmetry. Interestingly, we show that $\lambda_\mathrm{latt}$ provides a knob
that allows us to investigate the emergence of the SC phase at low
temperatures, as an instability from either a non-Fermi liquid or a Fermi
liquid normal state. The phase transitions between the SC and these normal
states are characterized by different critical exponents, which may also vary
for each gap symmetry. Finally, we argue that these results might explain the
dependence of $T_c$ in the vicinity of the nematic quantum critical point
exhibited by the compound FeSe$_{1 - x}$S$_x$.
