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