  Superconducting pnictides are widely found to feature spin-singlet pairing in
the vicinity of an antiferromagnetic phase, for which nesting between electron
and hole Fermi surfaces is crucial. LiFeAs differs from the other pnictides by
(i) poor nesting properties and (ii) unusually shallow hole pockets.
Investigating magnetic and pairing instabilities in an electronic model that
incorporates these differences, we find antiferromagnetic order to be absent.
Instead we observe almost ferromagnetic fluctuations which drive an instability
toward spin-triplet p-wave superconductivity.
