We present the first high-resolution spectra for the eclipsing binary V404Lyr 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_=7330{+/-}150K and a rotational velocity of v_1_sini=148{+/-}18km/s. The simultaneous analysis of our double-lined radial velocities and the pulsation-subtracted Kepler data gives us accurate stellar and system parameters of V404Lyr. The masses, radii, and luminosities are M1=2.17{+/-}0.06M_{sun}, R1=1.91{+/-}0.02R{sun}, and L1=9.4{+/-}0.8L{sun} for the primary, and M2=1.42{+/-}0.04M{sun}, R2=1.79{+/-}0.02R{sun}, and L2=2.9{+/-}0.2L{sun} for the secondary. The tertiary component orbiting the eclipsing pair has a mass of M_3b=0.71{+/-}0.15M_{sun} in an orbit of P_3b=642{+/-}3d, e_3b_=0.21{+/-}0.04, and a_3b_=509{+/-}2R_{sun}. 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 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.