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We report on high-precision atomic mass measurements of $^{148\text{-}153}$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 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 call for further studies to elucidate the structure of neutron-rich lanthanum isotopes.