This article presents differential measurements of the asymmetry between $\Lambda b0$ and $\Lambda ―b0$ baryon production rates in proton-proton collisions at centre-of-mass energies of $s=7$ and $8TeV$ collected with the LHCb experiment, corresponding to an integrated luminosity of $3fb-1$. The $\Lambda b0$ baryons are reconstructed through the inclusive semileptonic decay $\Lambda b0\to \Lambda c+\mu -\nu ―\mu X$. The production asymmetry is measured both in intervals of rapidity in the range and transverse momentum in . The results are found to be incompatible with symmetric production with a significance of 5.8 standard deviations for both $s=7$ and $8TeV$ data, assuming no $CP$ violation in the decay. There is evidence for a trend as a function of rapidity with a significance of 4 standard deviations. Comparisons to predictions from hadronisation models in PYTHIA and heavy-quark recombination are provided. This result constitutes the first observation of a particle-antiparticle asymmetry in $b$-hadron production at LHC energies.