  The lack of nesting of the electron and hole Fermi-surface sheets in the
Fe-based superconductor LiFeAs, with a critical temperature of 18 K, has led to
questions as to whether the origin of superconductivity in this material might
be different from other Fe-based superconductors. Both angle-resolved
photoemission and quasiparticle interference experiments have reported fully
gapped superconducting order parameters with significant anisotropy. The system
is also of interest because relatively strong correlations seem to be
responsible for significant renormalization of the hole bands. Here we present
calculations of the superconducting gap and pairing in the random-phase
approximation using Fermi surfaces derived from measured photoemission spectra.
The qualitative features of the gaps obtained in these calculations are shown
to be different from previous two-dimensional theoretical works, and in good
agreement with experiment on the main Fermi surface pockets. We analyze the
contributions to the pairing vertex thus obtained and show that the scattering
processes between electron and hole pockets that are believed to dominate the
pairing in other Fe-based superconductors continue to do so in LiFeAs despite
the lack of nesting, leading to gaps with anisotropic $s_\pm$ structure. Some
interesting differences relating to the enhanced $d_{xy}$ orbital content of
the LiFeAs Fermi surface are noted.
