  We present the first study of the production of a Standard Model Higgs boson
at a lepton collider in association with a pair of W bosons, $e^+_{} e^-_{} \to
W^+_{} W^-_{} H$, in the inverse seesaw model. Taking into account all relevant
experimental and theoretical constraints, we find sizable effects due to the
additional heavy neutrinos up to -38% on the total cross-section at a
center-of-mass energy of 3 TeV, and even up to -66% with suitable cuts. This
motivates a detailed sensitivity analysis of the process $e^+_{} e^-_{} \to
W^+_{} W^-_{} H$ as it could provide a new, very competitive experimental probe
of low-scale neutrino mass models.
