  Using the angle-resolved photoemission spectroscopy (ARPES) data accumulated
over the whole Brillouin zone (BZ) in LiFeAs we analyze the itinerant component
of the dynamic spin susceptibility in this system in the normal and
superconducting state. We identify the origin of the incommensurate magnetic
inelastic neutron scattering (INS) intensity as scattering between the electron
pockets, centered around the $(\pi,\pi)$ point of the BZ and the large
two-dimensional hole pocket, centered around the $\Gamma$-point of the BZ. As
the magnitude of the superconducting gap within the large hole pocket is
relatively small and angle dependent, we interpret the INS data in the
superconducting state as a renormalization of the particle-hole continuum
rather than a true spin exciton. Our comparison indicates that the INS data can
be reasonably well described by both the sign changing symmetry of the
superconducting gap between electron and hole pockets as well as sign
preserving gap, depending on the assumptions made for the fermionic damping.
