  The leading-order electromagnetic and strong isospin-breaking corrections to
the ratio of $K_{\mu 2}$ and $\pi_{\mu 2}$ decay rates are evaluated for the
first time on the lattice, following a method recently proposed. The lattice
results are obtained using the gauge ensembles produced by the European Twisted
Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical quarks. Systematics effects
are evaluated and the impact of the quenched QED approximation is estimated.
Our result for the correction to the tree-level $K_{\mu 2} / \pi_{\mu 2}$ decay
ratio is $-1.22\,(16) \%$ to be compared to the estimate $-1.12\,(21) \%$ based
on Chiral Perturbation Theory and adopted by the Particle Data Group.
