The production of $\Lambda^+_c$ baryons produced directly at the interacting
point is studied in proton-lead collisions collected with the LHCb detector at
the LHC. The data sample corresponds to an integrated luminosity of
$1.58\mathrm{nb}^{-1}$ recorded at a nucleon-nucleon centre-of-mass energy of
$\sqrt{s_{NN}}=5.02$ TeV. Measurements of the differential cross-section and
the forward-backward production ratio are reported for $\Lambda^+_c$ baryons
with transverse momenta in the range $2
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