  Gapped fermion theories with gapless boundary fermions can exist in any
number of dimensions. When the boundary has even space-time dimensions and
hosts chiral fermions, a quantum Hall current flows from the bulk to the
boundary in a background electric field. This current compensate for the
boundary chiral anomaly. Such a current inflow picture is absent when the
boundary theory is odd dimensional. However, in recent work, the idea of
quantum Hall current has been generalized to describe odd dimensional boundary
theories in continuous Euclidean space-time dimension of infinite volume. In
this paper we extend this idea to a lattice regulated finite volume theory of
1+1 dimensional Wilson-Dirac fermions. This fermion theory with a domain wall
in fermion mass can host gapless modes on the wall. The number of gapless
fermions is equal to the integral of the divergence of the lattice generalized
Hall current.
