  We study the deformation theory of the Fano scheme
$\mathrm{F}=\mathrm{F}(\mathrm{X})$ of lines on a cubic $\mathrm{X}$ of
dimension $d$ with only finitely many singularities. By taking the relative
Fano scheme, we define a morphism
$\eta:\mathscr{D}_{\mathrm{X}}\rightarrow\mathscr{D}_{\mathrm{F}}$ of the local
moduli functors associated to $\mathrm{X}$ and $\mathrm{F}$, respectively. We
show that for $d\geqslant 5$, $\eta$ yields an isomorphism on first-order
deformations; in particular, $\eta$ is an isomorphism whenever
$\mathrm{H}^{0}(\Theta_{\mathrm{X}})=0$.
