  We study how superconducting Tc is affected as an electronic system in a
tetragonal environment is tuned to a nematic quantum critical point (QCP).
Including coupling of the electronic nematic variable to the relevant lattice
strain restricts criticality only to certain high symmetry directions. This
allows a weak-coupling treatment, even at the QCP. We develop a criterion
distinguishing weak and strong Tc enhancements upon approaching the QCP. We
show that negligible Tc enhancement occurs only if pairing is dominated by a
non-nematic interaction away from the QCP, and simultaneously if the
electron-strain coupling is sufficiently strong. We argue this is the case of
the iron superconductors.
