  We address some issues relating to a supersymmetric (SUSY) Ward-Takahashi
(WT) identity in Sugino's lattice formulation of two-dimensional (2D)
$\mathcal{N}=(2,2)$ $SU(k)$ supersymmetric Yang-Mills theory (SYM). A
perturbative argument shows that the SUSY WT identity in the continuum theory
is reproduced in the continuum limit without any operator
renormalization/mixing and tuning of lattice parameters. As application of the
lattice SUSY WT identity, we show that a prescription for the hamiltonian
density in this lattice formulation, proposed by Kanamori, Sugino and Suzuki,
is justified also from a perspective of an operator algebra among
correctly-normalized supercurrents. We explicitly confirm the SUSY WT identity
in the continuum limit to the first nontrivial order in a semi-perturbative
expansion.
