Summary: In this paper, we analyze the Hawking radiation (HR) of a non-asymptotically flat (NAF) dyonic black hole (dBH) in four-dimensional (4D) Einstein-Maxwell-Dilaton (EMD) gravity by using one of the semiclassical approaches which is the so-called Hamilton-Jacobi (HJ) method. We particularly motivate on the isotropic coordinate system (ICS) of the dBH in order to highlight the ambiguity to be appeared in the derivation of the Hawking temperature \((T_{H})\) via the HJ method. Besides, it will be shown that the ICS allows us to write the metric of the dBH in form of the Fermat metric, which renders possible of identification of the refractive index \((n)\) of the dBH. It is unraveled that the value of \(n\) and therefore the gravitational lensing effect is decisive on the tunneling rate of the HR. We also uncloak how one can resolve the discrepancy about the \(T_{H}\) of the dBH in spite of that lensing effect.