  We propose a factorized approach to QED radiative corrections for inclusive
and semi-inclusive deep-inelastic scattering to systematically account for QED
and QCD radiation contributions to both processes on equal footing. This is
achieved by utilizing factorization to resum logarithmically enhanced QED
radiation into universal lepton distribution and fragmentation (or jet)
functions. Numerical simulations suggest that the QED effects induced by the
rotational distortion of the hadron transverse momentum, arising from the
mismatch between the experimental Breit frame and the true photon-hadron frame,
can be as large as 50\% for moderate $Q$, and become increasingly important for
large transverse momenta. Our framework provides a uniform treatment of
radiative effects for extracting three-dimensional hadron structure from
high-energy lepton-hadron scattering at current and future facilities, such as
the Electron-Ion Collider.
