Perovskite oxynitrides are, due to their reduced band gap compared to oxides, promising materials for photocatalytic applications. They are most commonly synthesized from {110} layered Carpy-Galy (A2B2O7) perovskites via thermal ammonolysis, i.e. the exposure to a flow of ammonia at elevated temperature. The conversion of the layered oxide to the non-layered oxynitride must involve a complex combination of nitrogen incorporation, oxygen removal and ultimately structural transition by elimination of the interlayer shear plane. Despite the process being commonly used, little is known about the microscopic mechanisms and hence factors that could ease the conversion. Here we aim to derive such insights via density functional theory calculations of the defect chemistry of the oxide and the oxynitride as well as the oxide's surface chemistry. Our results point to the crucial role of surface oxygen vacancies in forming clusters of NH3 decomposition products and in incorporating N, most favorably substitutionally at the anion site. N then spontaneously diffuses away from the surface, more easily parallel to the surface and in interlayer regions, while diffusion perpendicular to the interlayer plane is somewhat slower. Once incorporation and diffusion lead to a local N concentration of about 70% of the stoichiometric oxynitride composition, the nitridated oxide spontaneously transforms to a nitrogen-deficient oxynitride. Since anion vacancies are crucial for the nitrogen incorporation and diffusion as well as the transformation process, their concentration in the precursor oxide is a relevant tuning parameter to optimize the oxynitride's synthesis and properties.