  We construct an open enumerative theory for the Landau-Ginzburg (LG) model
$(\mathbb{C}^2, \mu_r\times \mu_s, x^r+y^s)$. The invariants are defined as
integrals of multisections of a Witten bundle with descendents over a moduli
space that is a real orbifold with corners. In turn, a generating function for
these open invariants yields the mirror LG model and a versal deformation of it
with flat coordinates. After establishing an open topological recursion result,
we prove an LG/LG open mirror symmetry theorem in dimension two with all
descendents. The open invariants we define are not unique but depend on
boundary conditions that, when altered, exhibit wall-crossing phenomena for the
invariants. We describe an LG wall-crossing group classifying the wall-crossing
transformations that can occur.
