We report on high-precision atomic mass measurements of ^{148-153}La and ^{151}Ce performed with the JYFLTRAP double Penning trap using the phase-imaging ion-cyclotron-resonance technique. The masses of ^{152,153}La were experimentally determined for the first time. We confirm the sharp kink in the two-neutron separation energies at the neutron number N=93 in the cerium (Z=58) isotopic chain. Our precision mass measurements of the most exotic neutron-rich lanthanum (Z=57) isotopes reveal a unexpected sudden increase in two-neutron separation energies from N=92 to N=93. Unlike in the cerium isotopic chain, the kink is not sharp but extends to N=94 forming a prominent bump. The gain in energy is about 0.4 MeV, making it one of the strongest changes in two-neutron separation energies over the whole chart of nuclides, away from nuclear shell closures. The results, correlated with a predicted onset of quadrupole deformation for N≥92, call for further studies to elucidate the structure of neutron-rich lanthanum isotopes.