  Let $T$ be a compact, metrisable and strongly countable-dimensional
topological space. Let $\mathcal{M}^T$ be the set of all metrics $d$ on $T$
compatible with its topology, and equip $\mathcal{M}^T$ with the topology of
uniform convergence, where the metrics are regarded as functions on $T^2$. We
prove that the set $\mathcal{A}^{T,1}$ of metrics $d\in\mathcal{M}^T$ for which
the Lipschitz-free space $\mathcal{F}(T,d)$ has the metric approximation
property is residual in $\mathcal{M}^T$.
