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The discovery of the new proton emitter $^{116}_{~57}$La$_{59}$, 23 neutrons away from the only stable La isotope, $^{139}_{~57}$La$_{82}$, is reported. The $^{116}$La nuclei were synthesised in the fusion-evaporation reaction $^{58}$Ni($^{64}$Zn, p4n)$^{116}$La and identified via their proton radioactivity using the MARA mass spectrometer and the silicon detectors placed at its focal plane. Comparisons of the measured proton energy ($E_{p} = 718 \pm 9 $ keV) and half-life ($T_{1/2} = 50 \pm 22$ ms) with values calculated using %microscopic nuclear barrier penetration theory the Universal Decay Law approach indicate that the proton is emitted with an orbital angular momentum $l=2$ and that its emission probability is enhanced relative to its closest, less exotic, odd-even lanthanum isotope ($^{117}_{~57}$La$_{60}$) while the proton-emission $Q$-value is lower. We propose this to be a signature for the presence of strong neutron-proton pair correlations in this exotic, neutron deficient system. The observations of $\gamma$ decays from isomeric states in $^{116}$La and $^{117}$La are also reported.