We present the first high-resolution spectra for the eclipsing binary V404 Lyr showing γ Dor pulsations, which we use to study its absolute properties. By fitting models to the disentangling spectrum of the primary star, we found that it has an effective temperature of T eff,1 = 7, 330 ± 150 K and a rotational velocity of v 1 sini = 148 ± 18 km s −1 . The simultaneous analysis of our double-lined radial velocities and the pulsation-subtracted Kepler data gives us accurate stellar and system parameters of V404 Lyr. The masses, radii, and luminosities are M 1 = 2.17±0.06 M ⊙ , R 1 = 1.91±0.02 R ⊙ , and L 1 = 9.4±0.8 L ⊙ for the primary, and M 2 = 1.42±0.04 M ⊙ , R 2 = 1.79±0.02 R ⊙ , and L 2 = 2.9±0.2 L ⊙ for the secondary. The tertiary component orbiting the eclipsing pair has a mass of M 3b = 0.71±0.15 M ⊙ in an orbit of P 3b = 642±3 days, e 3b = 0.21±0.04, and a 3b = 509±2 R ⊙ . The third light of l 3 = 4.1 ± 0.2% could be partly attributable to the K-type circumbinary object. By applying a multiple frequency analysis to the eclipsesubtracted light residuals, we detected 45 frequencies with signal to noise amplitude ratios larger than 4.0. Identified as independent pulsation modes, seven frequencies (f 1 − f 6 , f 9 ), their new pulsation constants, and the location in the Hertzsprung-Russell diagram indicate that the pulsating primary is a γ Dor-type variable star.