  Predictions are provided for double differential cross sections and
forward-backward ratios of $D^{0}$ production in $p\rm Pb$ (forward) and
$\rm{Pb}$$p$ (backward) collisions at 5.02~TeV. The effect of nuclear
corrections on the ratio of differential cross sections ratios is estimated to
be $\simeq$ (10-30)\% in the kinematically accessible region of LHCb, and
interestingly this ratio is approximately flat with respect to $p_T(D^0)$ due
to a compensation of shadowing and anti-shadowing effects arising from the
input nuclear PDFs. In comparison to $J/\psi(\rightarrow\mu^-\mu^+)$
measurements which have already been performed with the available data, the
cross section for $D^{0}(\rightarrow K^-\pi^+)$ production is expected to be
two-orders of magnitude higher.
