  We construct a conformal lattice theory with only gauge degrees of freedom
based on the induced non-local gauge action in QED$_3$ coupled to large number
of flavors $N$ of massless two-component Dirac fermions. This lattice system
displays signatures of criticality in gauge observables, without any
fine-tuning of couplings and can be studied without Monte Carlo critical
slow-down. By coupling exactly massless fermion sources to the lattice gauge
model, we demonstrate that non-trivial anomalous dimensions are induced in
fermion bilinears depending on the dimensionless electric charge of the
fermion. We present a proof-of-principle lattice computation of the
Wilson-coefficients of various fermion bilinear three-point functions. Finally,
by mapping the charge $q$ of fermion in the model to a flavor $N$ in massless
QED$_3$, we point to an universality in low-lying Dirac spectrum and an
evidence of self-duality of $N=2$ QED$_3$.
