  We report fully momentum dependent, self-consistent calculations of the gap
symmetry, Fermi surface (FS) anisotropy and Tc of superconducting (SC) LiFeAs
using the experimental band structure and a realistic small-q electron phonon
interaction within the framework of Migdal-Eliashberg theory. In the
stoichiometric regime, we find the exact s++ gap as reported by ARPES. For
slight deviations from stoichiometry towards electron doping, we find that a
chiral triplet p_x+ip_y state stabilizes near Tc and that at lower temperatures
a transition from the triplet to singlet s+- SC takes place. Further doping
stabilizes the chiral p-wave SC down to T=0. Precisely the same behavior was
observed recently by NMR. Our results provide a natural and universal
understanding of the conflicting experimental observations in LiFeAs.
