We describe a first-principles method to apply lattice QCD to compute the order $\alpha_{\mathrm{EM}}$ corrections to $K\to\pi\ell\nu_\ell$ decay. This method formulates the calculation in infinite volume with the conventional infinite-volume, continuum treatment of QED. Infinite volume reconstruction is used to replace the QCD components of the calculation with finite-volume amplitudes which can be computed in Euclidean space using lattice QCD,
introducing finite-volume errors which vanish exponentially as the volume used in the QCD calculation is increased. This approach has also been described in an appendix to the recent paper: Phys.Rev.D 108 (2023) 1, 014501.