  A generalized effective spin-chain model is developed for studies of strongly
interacting spinor gases in a one-dimensional (1D) optical lattice. The spinor
gas is mapped to a system of spinless fermions and a spin-chain. A generalized
effective spin-chain Hamiltonian that acts on the mapped system is developed to
study the static and dynamic properties of the spinor gas. This provides a
computationally efficient alternative tool to study strongly interacting spinor
gases in 1D lattice systems. This formalism permits the study of spinor gases
with arbitrary spin and statistics, providing a generalized approach for 1D
strongly interacting gases. By virtue of its simplicity, it provides an easier
tool to study and gain deeper insights into the system. In combination with the
model defined previously for continuum systems, a unified framework is
developed. Studying the mapped system using this formalism recreates the
physics of spinor gas in 1D lattice. Additionally, the time evolution of a
quenched system is studied. The generalized effective spin-chain formalism has
potential applications in the study of a multitude of interesting phenomena
arising in lattice systems such as high-$T_c$ superconductivity and the
spin-coherent \& spin-incoherent Luttinger liquid regimes.
