  We describe a scheme for constructing generating sets for Kronheimer and
Mrowka's singular instanton knot homology for the case of knots in lens spaces.
The scheme involves Heegaard-splitting a lens space containing a knot into two
solid tori. One solid torus contains a portion of the knot consisting of an
unknotted arc, as well as holonomy perturbations of the Chern-Simons functional
used to define the homology theory. The other solid torus contains the
remainder of the knot. The Heegaard splitting yields a pair of Lagrangians in
the traceless $SU(2)$-character variety of the twice-punctured torus, and the
intersection points of these Lagrangians comprise the generating set that we
seek. We illustrate the scheme by constructing generating sets for several
example knots. Our scheme is a direct generalization of a scheme introduced by
Hedden, Herald, and Kirk for describing generating sets for knots in $S^3$ in
terms of Lagrangian intersections in the traceless $SU(2)$-character variety
for the 2-sphere with four punctures.
