  We develop an effective quantum electrodynamics for non-Hermitian (NH) Dirac
materials interacting with photons. These systems are described by nonspatial
symmetry protected Lorentz invariant NH Dirac operators, featuring two velocity
parameters $v_{_{\rm H}}$ and $v_{_{\rm NH}}$ associated with the standard
Hermitian and a masslike anti-Hermitian Dirac operators, respectively. They
display linear energy-momentum relation, however, in terms of an effective
Fermi velocity $v_{_{\rm F}}=\sqrt{v^2_{_{\rm H}}-v^2_{_{\rm NH}}}$ of NH Dirac
fermions. Interaction with the fluctuating electromagnetic radiation then gives
birth to an emergent Lorentz symmetry in this family of NH Dirac materials in
the deep infrared regime, where the system possesses a unique terminal velocity
$v_{_{\rm F}}=c$, with $c$ being the speed of light. While in two dimensions
such a terminal velocity is set by the speed of light in the free space,
dynamic screening in three spatial dimensions permits its nonuniversal values.
Manifestations of such an emergent spacetime symmetry on the scale dependence
of various physical observables in correlated NH Dirac materials are discussed.
