Excited states have been observed for the first time in the very neutron-deficient odd-odd nucleus 57120La63. The observed γ rays have been assigned based on coincidences with lanthanum X rays measured with the JUROGAM 3 array and with A=120 fusion-evaporation residues measured with the MARA separator. The observed γ rays form a rotational band which decays to the ground state via a cascade of four low-energy transitions. Based on the systematic comparisons with the heavier odd-odd La isotopes we assign spin-parity 4+ to the ground state and a πh11/2⊗νh11/2 configuration to the rotational band. The nuclear shape has been investigated by the cranked Nilsson-Strutinsky model. Two quasiparticle plus triaxial rotor model calculations including the np interaction nicely reproduce the spin of the inversion between the even- and odd-spin cascades of E2 transitions, giving credit to the np interaction as an important parameter responsible for the mechanism inducing the inversion. The position of the Fermi levels, in particular for neutrons, also has a strong impact on the observed inversion in the chain of lanthanum nuclei.