  The origin of spontaneous electronic nematic ordering provides important
information for understanding iron-based superconductors. Here, we analyze a
scenario where the $d_{xy}$ orbital strongly contributes to nematic ordering in
FeSe. We show that the addition of $d_{xy}$ nematicity to a pure
$d_{xz}/d_{yz}$ order provides a natural explanation for the unusual Fermi
surface and correctly reproduces the strongly anisotropic momentum dependence
of the superconducting gap. We predict a Lifshitz transition of an electron
pocket mediated by temperature and sulphur doping, whose signatures we discuss
by analysing available experimental data. We present the variation of momentum
dependence of the superconducting gap upon suppression of nematicity. Our
quantitatively accurate model yields the transition from tetragonal to nematic
FeSe and the FeSe$_{1-x}$S$_{x}$ series, and puts strong constraints on
possible nematic mechanisms.
