Given a simple, finite, directed graph $G$, let's call a $2$-coloring of the vertices of $G$ is *friendly* if every vertex has an out-neighbour of the same color (while not all vertices are same-colored).

Broadly speaking, I wonder what graphs admit a friendly coloring. To be more specific:

Is it true that every simple, finite, directed graph with the minimum outdegree $3$ has a friendly coloring? If this is false, does there exist an integer $k\ge 4$ such that every directed graph with the minimum outdegree $k$ has a friendly coloring? If so, what is the smallest $k$ with this property?

The case $k=2$ is easy, but already the case $k=3$ seems nontrivial to me.

The same questions can also be asked for three or more colors.