  Building on work by Alishahi-Dowlin, we extract a new knot invariant $\lambda
\ge 0$ from universal Khovanov homology. While $\lambda$ is a lower bound for
the unknotting number, in fact more is true: $\lambda$ is a lower bound for the
proper rational unknotting number (the minimal number of rational tangle
replacements preserving connectivity necessary to relate a knot to the unknot).
Moreover, we show that for all $n \ge 0$, there exists a knot K with
$\lambda(K) = n$. Along the way, following Thompson, we compute the Bar-Natan
complexes of rational tangles.
