Angular-dependent de Haas-van Alphen measurements allow the mapping of Fermi surfaces in great detail with high accuracy. Density functional electronic-structure calculations can be carried out with high precision, but depend crucially on the used structural information and the applied calculational approximations. We report in a detailed study the sensitivity of the calculated electronic band structure of the 122 compound LaFe₂P₂ on (i) the exact P position in the unit cell, parametrized by a so-called z parameter, and on (ii) the treatment of the La 4f  states. Depending on the chosen exchange and correlation-potential approximation, the calculated z parameter varies slightly and corresponding small but distinctive differences in the calculated band structure and Fermi-surface topology appear. Similarly, topology changes appear when the energy of the mostly unoccupied La 4f  states is corrected regarding their experimentally observed position. The calculated results are compared to experimental de Haas-van Alphen data. Our findings show a high sensitivity of the calculated band structure on the pnictide z position and the need for an accurate experimental determination of this parameter at low temperatures, and a particular need for a sophisticated treatment of the La 4f  states. Thus, this is not only crucial for the special case of LaFe₂P₂ studied here, but of importance for the precise determination of the band structure of related 122 materials and La containing compounds in general.