  We present a phenomenological study of photon-initiated (PI) lepton
production at the LHC, as implemented in the structure function (SF) approach.
We provide detailed predictions for multi-differential lepton pair production,
and show that the impact on observables sensitive to the the weak mixing angle,
$\sin^2 \theta_W$, and $W$ boson mass, $M_W$, as well as PDFs can be
non-negligible, in particular given the high precision being aimed for. The SF
calculation automatically provides percent level precision in the corresponding
production cross section across all relevant regions of phase space, in a
manner that cannot be straightforwardly achieved by alternative approaches. It
is therefore uniquely positioned to account for LHC precision requirements. In
addition to the pure $\gamma\gamma$ channel, we include initial-state $Z$ as
well as mixed $\gamma /Z + q$ contributions, and assess their impact. We also
consider photon-initiated lepton-lepton scattering, and again find the SF
approach can provide high precision predictions for this process in way that
can straightforwardly account for any fiducial cuts imposed. Finally, we
provide a publicly available Monte Carlo generator, SFGen, for PI lepton pair
production and lepton-lepton scattering within the SF approach, for use by the
community.
