  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 can provide percent level precision in the corresponding production
cross sections, and is therefore well positioned to account for LHC precision
requirements. We consider the pure $\gamma\gamma$ channel, and compare in
detail to the NLO collinear calculation. We in addition 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.
