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We develop a methodology for the computation of $K\ensuremath{\rightarrow}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}{{\ensuremath{\ell}}^{\ensuremath{'}}}^{+}{{\ensuremath{\ell}}^{\ensuremath{'}}}^{\ensuremath{-}}$ decay width using lattice QCD and present an exploratory study here. use scalar function method to account momentum dependence amplitude adopt infinite-volume reconstruction reduce systematic errors such as temporal truncation effects finite-volume effects. then perform four-body phase-space integral obtain width. The only remaining technical problem is possible power-law associated with process $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}\ensuremath{\rightarrow}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}{{\ensuremath{\ell}}^{\ensuremath{'}}}^{+}{{\ensuremath{\ell}}^{\ensuremath{'}}}^{\ensuremath{-}}$, where intermediate state involves multiple hadrons. In this work, we gauge ensemble twisted-mass fermion pion mass ${m}_{\ensuremath{\pi}}=352\text{ }\text{ }\mathrm{MeV}$ nearly physical kaon mass. At kinematics, $\ensuremath{\pi}\ensuremath{\pi}$ in cannot be on shell simultaneously, $2{m}_{\ensuremath{\pi}}&gt;{m}_{K}$, are exponentially suppressed. Using developed methods mentioned above, calculate branching ratios four channels $K\ensuremath{\rightarrow}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}{{\ensuremath{\ell}}^{\ensuremath{'}}}^{+}{{\ensuremath{\ell}}^{\ensuremath{'}}}^{\ensuremath{-}}$, results comparable experimental measurements ChPT predictions. Our work demonstrates capability improve Standard Model prediction