  We study a three-dimensional non-compact QED with a single two-component
massless fermion and two infinitely massive regulator fermions of half the
charge using lattice overlap formalism. The parity anomaly is expected to
cancel exactly between the massless and regulator fermions in the continuum,
but this cancellation is inexact on lattice akin to lattice chiral gauge
theories. We show non-perturbatively that parity-breaking terms vanish in the
continuum limit at any finite volume. We present numerical evidences that the
resulting parity-invariant theory spontaneously breaks parity in the infinite
volume limit.
