It is theoretically shown that the coherent hopping dynamics of a non-relativistic particle in engineered tight-binding lattices subjected to combined ac and dc driving forces can mimic in Fock space relativistic quantum field theories (QFTs) of strongly interacting fields, enabling access to extreme dynamical regimes beyond weak coupling and perturbative predictions. In particular, the simulation of a QFT model describing a Dirac field strongly coupled to a scalar bosonic field via a Yukawa coupling is proposed, suggesting the possibility of implementing this model using engineered lattices of evanescently coupled optical waveguides with a bent optical axis.