Xiao's hyperellipticity conjecture for Lefschetz fibrations

Let $f$ be a genus-$g$ Lefschetz fibration with slope $\lambda_f$, and call $f$ hyperelliptic when its monodromy lies in the hyperelliptic mapping class group. Xiao's hyperellipticity conjecture. If

$$\lambda_f=4-\frac{4}{g},$$

then $f$ is hyperelliptic. The source says that this conjecture is raised for holomorphic Lefschetz fibrations over curves of any nonnegative genus. It also explains that the paper gives a counterexample in the broader Lefschetz-fibration setting, so the claim must be understood with Xiao's holomorphic hypotheses.