  Dowdall and Taylor observed that given a finite-index subgroup of a free
group, taking covers induces an embedding from the Outer Space of the free
group to the Outer Space of the subgroup, that this embedding is an isometry
with respect to the (asymmetric) Lipschitz metric, and that the embedding sends
folding paths to folding paths. The purpose of this note is to extend this
result to virtually free groups. We further extend a result Francaviglia and
Martino, proving the existence of "candidates" for the Lipschitz distance
between points in the Outer Space of the virtually free group. Additionally we
identify a deformation retraction of the spine of the Outer Space for the
virtually free group with the space considered by Krsti\'c and Vogtmann.
