We present a study of six far-infrared fine structure lines in the z = 4.225 lensed dusty star-forming galaxy SPT 0418−47 to probe the physical conditions of its interstellar medium (ISM). In particular, we report Atacama Pathfinder EXperiment (APEX) detections of the [OI] 145 μm and [OIII] 88 μm lines and Atacama Compact Array (ACA) detections of the [NII] 122 and 205 μm lines. The [OI] 145 μm/[CII] 158 μm line ratio is ∼5× higher compared to the average of local galaxies. We interpret this as evidence that the ISM is dominated by photo-dissociation regions with high gas densities. The line ratios, and in particular those of [OIII] 88 μm and [NII] 122 μm imply that the ISM in SPT 0418−47 is already chemically enriched to nearly solar metallicity. While the strong gravitational amplification was required to detect these lines with APEX, larger samples can be observed with the Atacama Large Millimeter/submillimeter Array (ALMA), and should allow observers to determine if the dense, solar metallicity ISM is common among these highly star-forming galaxies.