  We demonstrate how probes of CP-violating observables in Higgs di-tau decays
at prospective future lepton colliders could provide a test of weak scale
baryogenesis with significant discovery potential. Measurements at the Circular
Electron Positron Collider, for example, could exclude a CP phase larger than
$2.9^\circ$ ($5.6^\circ$) at 68% (95%) C.L. assuming the Standard Model value
for magnitude of the tau lepton Yukawa coupling. Conversely, this sensitivity
would allow for a $5\,\sigma$ discovery for 82% of the CP phase range
$[0,2\pi)$. The reaches of the Future Circular Collider - ee and International
Linear Collider are comparable. As a consequence, future lepton colliders could
establish the presence of CP violation required by lepton flavored electroweak
baryogenesis with at least $3\,\sigma$ sensitivity. Our results illustrate that
Higgs factories are not just precision machines but can also make $\mathcal
O(1)$ measurement of the new physics beyond the Standard Model.
