  We show that the canonical-lift construction for ordinary elliptic curves
over perfect fields of characteristic $p>0$ extends uniquely to arbitrary
families of ordinary elliptic curves, even over $p$-adic formal schemes. In
particular, the universal ordinary elliptic curve has a canonical lift. The
existence statement is largely a formal consequence of the universal property
of Witt vectors applied to the moduli space of ordinary elliptic curves, at
least with enough level structure. As an application, we show how this point of
view allows for more formal proofs of recent results of Finotti and
Erdo\u{g}an.
