  Recent results indicate that charm quarks are intrinsic components of the
proton wave function, and that the charm and anticharm distributions for a
given value of the Bjorken - $x$ variable can be different. In this paper, we
will investigate the impact of this asymmetric intrinsic charm on the
production of $D^0$ and ${\bar D}^0$ mesons for fixed target $p \!+
^{20}\!\!Ne$ collisions at the LHCb. In our calculations, we include the
contribution of the gluon-gluon fusion, gluon - charm and recombination
processes and assume distinct models for the treatment of the intrinsic charm
component. We demonstrate that the presence of an intrinsic charm improves the
description of the current data for the rapidity and transverse momentum
distributions of $D$ mesons. However, such models are not able to describe the
LHCb data for the $D^0$-${\bar D}^0$ asymmetry at large transverse momentum,
which point out that the description of the intrinsic charm needs to be
improved and/or new effects should be taken into account in the production of
heavy mesons at forward rapidities in fixed - target collisions.
