  This is the third of the series of articles on the large-$N$ two-dimensional
$\mathbb{CP}^{N-1}$ sigma model, defined on a finite space interval $L$ with
Dirichlet boundary conditions. Here the cases of the general Dirichlet boundary
conditions are studied, where the relative $\mathbb{CP}^{N-1}$ orientations at
the two boundaries are generic, and numerical solutions are presented.
Distinctive features of the $\mathbb{CP}^{N-1}$ sigma model, as compared e.g.,
to an $O(N)$ model, which were not entirely evident in the basic properties
studied in the first two articles in the large $N$ limit, manifest themselves
here. It is found that the total energy is minimized when the fields are
aligned in the same direction at the two boundaries.
