Wave-function-based ab initio calculations on the lowest states of the 4f(n),4f(n-1)5d(t2g)1, and 4f(n-1)5d(e(g))1 configurations of (LnCl6)3- clusters (Ln=Ce to Tb) embedded in the cubic elpasolite Cs2NaYCl6 have been performed, in an attempt to contribute to a comprehensive understanding of the 4f-->5d excitations of lanthanide ions in crystals. Reliable data are provided on the changes of bond lengths and breathing mode vibrational frequencies upon 4f-->5d(t2g) and 4f-->5d(e(g)) excitations, as well as on minimum-to-minimum and vertical absorption and emission transitions, and on the Stokes shifts. The available experimental data are discussed and predictions are made. The stabilization of the 4f-->5d(baricenter) excitation of the doped ions with respect to the 4f-->5d excitations of the free ions, which is a key variable for the understanding of these excitations in solid hosts, is analyzed and found to be due, in two-thirds, to dynamic ligand correlation effects and, in one-third, to orbital relaxation, charge transfer, and covalency effects present in a mean-field approximation.