This article presents differential measurements of the asymmetry between $\Lambda_b^0$ and $\overline{\Lambda}_b^0$ baryon production rates in proton-proton collisions at centre-of-mass energies of $\sqrt{s}=7$ and $8\,\textrm{TeV}$ collected with the LHCb experiment, corresponding to an integrated luminosity of $3\,\textrm{fb}^{-1}$. The $\Lambda_b^0$ baryons are reconstructed through the inclusive semileptonic decay $\Lambda_b^0\rightarrow\Lambda_c^+\mu^-\overline{\nu}_{\mu}X$. The production asymmetry is measured both in intervals of rapidity in the range $2.15
$\Lambda_{b}^{0}$ production asymmetry in bins of $\Lambda_{b}^{0}$ rapidity for proton-proton collisions at $\sqrt{s} = 7$ TeV. The first uncertainty is statistical and the second represents the systematic uncertainty. The results in neighbouring intervals are correlated.
$\Lambda_{b}^{0}$ production asymmetry in bins of $\Lambda_{b}^{0}$ rapidity for proton-proton collisions at $\sqrt{s} = 8$ TeV. The first uncertainty is statistical and the second represents the systematic uncertainty. The results in neighbouring intervals are correlated.
$\Lambda_{b}^{0}$ production asymmetry in bins of $\Lambda_{b}^{0}$ $p_T$ for proton-proton collisions at $\sqrt{s} = 7$ TeV. The first uncertainty is statistical and the second represents the systematic uncertainty. The results in neighbouring intervals are correlated.
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