Antiprotonic atoms are ideal systems to study strong-field quantum electrodynamics (QED) since bound antiprotons orbit significantly closer to the nucleus compared to electrons due to their larger mass. As a result, these systems experience stronger fields and enhanced QED effects which will be used by the PAX experiment at CERN to perform more precise tests of strong-field QED by measuring transitions between circular Rydberg states in heavy antiprotonic atoms. We present improved theoretical calculations of the Lamb shift in antiprotonic atoms, which are required to use the data that will be produced by PAX to its full potential as a QED test. In particular, we present non-perturbative calculations of the vacuum polarization, which is strongly enhanced in antiprotonic atoms compared to their electronic counterparts.