Outlook for the Theoretical Precision of the Luminosity at Future Lepton Colliders

The LEP precision physics requirements on the theoretical precision tag for the respective luminosity were $0.054\mathrm{\%}$ ($0.061\mathrm{\%}$) at $M_Z$, where the former (latter) LEP result has (does not have) the pairs correction. For the contemplated FCC-ee, ILC, and CEPC Higgs/EW factories, one needs improvement at $M_Z$ to at least $0.01\mathrm{\%}$ for the theoretical precision tag. We discuss the paths one may take to even exceed this latter goal and present an update on the current expectations for both $M_Z$ and proposed higher energy scenarios.