  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 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.
