  Given a log Calabi-Yau surface $Y$ with maximal boundary $D$ and
distinguished complex structure, we explain how to construct a mirror Lefschetz
fibration $w: M \to \mathbb{C}$, where $M$ is a Weinstein four-manifold, such
that the directed Fukaya category of $w$ is isomorphic to $D^b \text{Coh}(Y)$,
and the wrapped Fukaya category $D^b\mathcal{W} (M)$ is isomorphic to $D^b
\text{Coh}(Y \backslash D)$. We construct an explicit isomorphism between $M$
and the total space of the almost-toric fibration arising in the work of
Gross-Hacking-Keel; when $D$ is negative definite this is expected to be the
Milnor fibre of a smoothing of the dual cusp of $D$. We also match our mirror
potential $w$ with existing constructions for a range of special cases of
$(Y,D)$, notably in work of Auroux-Katzarkov-Orlov and Abouzaid.
