  The metric dimension is quite a well-studied graph parameter. Recently, the
adjacency dimension and the local metric dimension have been introduced and
studied. In this paper, we give a general formula for the local metric
dimension of the lexicographic product $G \circ \mathcal{H}$ of a connected
graph $G$ of order $n$ and a family $\mathcal{H}$ composed by $n$ graphs. We
show that the local metric dimension of $G \circ \mathcal{H}$ can be expressed
in terms of the true twin equivalence classes of $G$ and the local adjacency
dimension of the graphs in $\mathcal{H}$.
