The higher order (HO) correlation beyond the coupled-cluster single double (triple) CCSD(T) level of theory, second-order spin-orbit coupling (SOC), and core-valence (CV) correlation effects on bond length, re, vibrational frequency, ωe, and dissociation energy, De, are studied for a set of 17 lanthanide containing diatomics, including lanthanum, europium, ytterbium, and lutetium oxides and halides. Convergence in the magnitudes of the SOC, CV, and HO corrections with respect to basis set size is examined using a sequence of double, triple, and quadruple-ζ basis sets, with the complete basis set (CBS) limit estimates provided in most cases. The CV effects on De, re, and ωe are calculated to amount up to 1.3 kcal·mol-1, 0.008 Å, and 5 cm-1, respectively. A detailed analysis of the origin of the CV effect with a particular accounting for various subvalence shells reveals that, generally, the Ln 4d correlation makes a major contribution, although in some instances the lower-lying 4sp shells contribute largely and even more substantially than 4d. The second-order SOC effect evaluated via two-component and four-component relativistic techniques proves to be non-negligible, especially for heavier species, e.g., LaI, in which it is as large as 0.8 kcal·mol-1 in De, 0.002 Å in re, and 1.3 cm-1 in ωe. Higher order correlation effects assessed through the CCSDT(Q) level are mostly less than 0.8 kcal·mol-1, 0.004 Å, and 5 cm-1; however, in species with prominence of nondynamical correlation, e.g., EuO, YbF, and LuO, the HO correction can amount to 1.2-1.6 kcal·mol-1, 0.005-0.008 Å, and 8-30 cm-1 in De, re, and ωe, respectively. In general, the [CCSD(T)+CV]/CBS + SOC + HO composite results are in good agreement with the available experimental data, exhibiting a mean absolute deviation of 1.8 kcal·mol-1 in De, 0.0023 Å in re, and 3.5 cm-1 in ωe. A significant experimental outlier, the bond length in YbI, is revealed, implying the need for re-examination of the experimental data.