We present the first high-resolution spectra for the eclipsing binary V404 Lyr showing \gamma 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 \pm 150 K and a rotational velocity of v _ { 1 } \sin i = 148 \pm 18 km s ^ { -1 } . The simultaneous analysis of our double-lined radial velocities and the pulsation-subtracted { \it Kepler } data gives us accurate stellar and system parameters of V404 Lyr . The masses , radii , and luminosities are M _ { 1 } = 2.17 \pm 0.06 M _ { \odot } , R _ { 1 } = 1.91 \pm 0.02 R _ { \odot } , and L _ { 1 } = 9.4 \pm 0.8 L _ { \odot } for the primary , and M _ { 2 } = 1.42 \pm 0.04 M _ { \odot } , R _ { 2 } = 1.79 \pm 0.02 R _ { \odot } , and L _ { 2 } = 2.9 \pm 0.2 L _ { \odot } for the secondary . The tertiary component orbiting the eclipsing pair has a mass of M _ { 3 b } = 0.71 \pm 0.15 M _ { \odot } in an orbit of P _ { 3 b } = 642 \pm 3 days , e _ { 3 b } = 0.21 \pm 0.04 , and a _ { 3 b } = 509 \pm 2 R _ { \odot } . The third light of l _ { 3 } = 4.1 \pm 0.2 \% could be partly attributable to the K-type circumbinary object . By applying a multiple frequency analysis to the eclipse-subtracted 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 \gamma Dor-type variable star .