  We use neutron scattering to study spin excitations in single crystals of
LiFe$_{0.88}$Co$_{0.12}$As, which is located near the boundary of the
superconducting phase of LiFe$_{1-x}$Co$_{x}$As and exhibits non-Fermi-liquid
behavior indicative of a quantum critical point. By comparing spin excitations
of LiFe$_{0.88}$Co$_{0.12}$As with a combined density functional theory (DFT)
and dynamical mean field theory (DMFT) calculation, we conclude that
wave-vector correlated low energy spin excitations are mostly from the $d_{xy}$
orbitals, while high-energy spin excitations arise from the $d_{yz}$ and
$d_{xz}$ orbitals. Unlike most iron pnictides, the strong orbital selective
spin excitations in LiFeAs family cannot be described by anisotropic Heisenberg
Hamiltonian. While the evolution of low-energy spin excitations of
LiFe$_{1-x}$Co$_x$As are consistent with electron-hole Fermi surface nesting
condition for the $d_{xy}$ orbital, the reduced superconductivity in
LiFe$_{0.88}$Co$_{0.12}$As suggests that Fermi surface nesting conditions for
the $d_{yz}$ and $d_{xz}$ orbitals are also important for superconductivity in
iron pnictides.
