The recently discovered Fe-based superconductor (FeBS) LaFe_{2}As_{2} seems to break away from an established pattern that doping an FeBS beyond 0.2e/Fe destroys superconductivity. LaFe_{2}As_{2} has an apparent doping of 0.5e, yet superconducts at 12.1 K. Its Fermi surface bears no visual resemblance with the canonical FeBS fermiology. It also exhibits two phases, none magnetic and only one superconducting. We show that the difference between them nonetheless has a magnetic origin, the one featuring disordered moments, and the other locally nonmagnetic. We find that La there assumes an unusual valence of +2.6 to +2.7, so that the effective doping is reduced to 0.30-0.35e. A closer look reveals the same key elements: hole Fermi surfaces near Γ-Z and electron ones near the X-P lines, with the corresponding peak in susceptibility, and a strong tendency to stripe magnetism. The physics of LaFe_{2}As_{2} is thus more similar to the FeBS paradigm than hitherto appreciated.