The X‐ray production (XRP) cross sections for the 66Dy Lk (k = l, α, η, β2,6,7,15, β1,6, β1,3,4,6, β2,7,15, γ1,5, γ2,3) emission lines have been measured by tuning the incident synchrotron radiation at energies over the range 7.8–9.2 keV and ~10–370 eV above the respective Li (i = 1–3) absorption edges. These measurements aim to check the reliability of the independent particle approximation models used to generate the theoretical data sets of different physical parameters required to calculate the XRP cross sections and also investigate the influence of many body effects on the photoionization process. The measured values have been compared with 4 sets of XRP cross sections calculated using the Dirac–Fock model‐based X‐ray emission rates, 2 sets of the Li (i = 1–3) subshell photoionization cross sections deduced from the self‐consistent Dirac–Hartree–Fock model‐based values and the nonrelativistic Hartree–Fock–Slater model‐based values, and 2 sets of the fluorescence (ωi) and Coster–Kronig (fij) yields. The present measured Lγ2,3 (originating from decay of the L1 subshell vacancies) XRP cross sections are found to be significantly higher than different sets of theoretical values, whereas a good agreement is generally observed for the various other XRP cross sections and relative intensities.