We construct a conformal lattice theory with only gauge degrees of freedom based on the induced nonlocal 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 slowdown. By coupling exactly massless fermion sources to the lattice gauge model, we demonstrate that nontrivial 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 a universality in low-lying Dirac spectrum and an evidence of self-duality of N=2 QED_{3}.