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We consider the three-dimensional Dirac operator coupled with a combinationof electrostatic and Lorentz scalar $\delta$-shell interactions. We approximatethis operator with general local interactions $V$. Without any hypotheses ofsmallness on the potential $V$, converges in the strong resolvent sense to theDirac Hamiltonian coupled with a $\delta$-shell potential supported on $\S$, abounded smooth surface. However, the coupling constant depends nonlinearly onthe potential $V.$

On the approximation of the $\delta$-shell interaction for the 3-D Dirac operator