  We develop the theory of a metric completion of an asymmetric metric space.
We characterize the points on the boundary of Outer Space that are in the
metric completion of Outer Space with the Lipschitz metric. We prove that the
simplicial completion, the subset of the completion consisting of simplicial
tree actions, is homeomorphic to the free splitting complex. We use this to
give a new proof of a theorem by Francaviglia and Martino that the isometry
group of Outer Space is homeomorphic to $\text{Out}(F_n)$ for $n \geq 3$ and
equal to $\text{PSL}(2,\mathbb{Z})$ for $n=2$.
