We present an ab initio calculation of the longitudinal electron scattering response function off He4 with two- and three-nucleon forces and compare to experimental data. The full four-body continuum dynamics is considered via the Lorentz integral transform method. The importance of the final-state interaction is shown at various energies and momentum transfers q. The three-nucleon force reduces the quasielastic peak by 10% for q between 300 and 500MeV/c. Its effect increases significantly at lower q, up to about 40% at q=100MeV/c. At very low q, however, data are missing.