  We propose a lattice-QCD-suitable framework for computing the two-photon
long-distance contribution to the complex $K_{\rm L}\rightarrow\mu^+\mu^-$
decay amplitude, where QED is treated perturbatively in the continuum and
infinite-volume. We provide preliminary numerical results on the
quark-connected diagrams on one ensemble at physical pion mass from this
method, with well-controlled systematic errors. The successful application of
this method will allow the determination of the dispersive part of the
aforementioned contribution from first-principles and enable a meaningful
comparison between the Standard-Model prediction and experiment.
