  We present quenched lattice QCD results for the contribution of higher-twist
operators to the lowest non-trivial moment of the pion structure function. To
be specific, we consider the combination $F_2^{\pi^+} + F_2^{\pi^-} - 2
F_2^{\pi^0}$ which has $I = 2$ and receives contributions from 4-Fermi
operators only. We introduce the basis of lattice operators. The
renormalization of the operators is done perturbatively in the $\bar{\rm{MS}}$
scheme using the 't Hooft-Veltman prescription for $\gamma_5$, taking
particular care of mixing effects. The contribution is found to be of
$O(f_\pi^2/Q^2)$, relative to the leading contribution to the moment of
$F_2^{\pi^+}$.
