Context. The formation of cosmic structures culminates with the assembly of galaxy clusters, a process that is quite different from cluster to cluster. Aims. We present the study of the structure and dynamics of the Lyra complex, consisting of the two clusters RXC J1825.3+3026 and CIZA J1824.1+3029, which was very recently studied by using both X-ray and radio data. Methods. This is the first analysis based on the kinematics of member galaxies. New spectroscopic data for 285 galaxies were acquired at the Italian Telescopio Nazionale Galileo and were used in combination with PanSTARRS photometry. The result of our member selection is a sample of 198 galaxies. Results. For RXCJ1825 and CIZAJ1824 we report the redshifts, z = 0.0645 and z = 0.0708, the first estimates of velocity dispersion, σ_v = 995⁺¹³¹₋₁₂₅ km s⁻¹ and σ_v = 700 ± 50 km s⁻¹, and of dynamical mass, M₂₀₀ = 1.1 ± 0.4 × 10¹⁵ M_⊙ and M₂₀₀ = 4 ± 0.1 × 10¹⁴ M_⊙. The past assembly of RXCJ1825 is traced by the two dominant galaxies, which are both aligned with the major axis of the galaxy distribution along the east–west direction, and by a minor northeast substructure. We also detect a quite peculiar high velocity field in the southwest region of the Lyra complex. This feature is likely related to a very luminous galaxy, which is characterized by a high velocity. This galaxy is suggested to be the central galaxy of a group that is in interaction with RXCJ1825 according to very recent studies based on X-ray and radio data. The redshift of the whole Lyra complex is z = 0.067. Assuming that the redshift difference between RXCJ1825 and CIZAJ1824 is due to the relative kinematics, the projected distance between the cluster centers is D ∼ 1.3 Mpc and the line–of–sight velocity difference is ∼1750 km s⁻¹. A dynamical analysis of the system shows that the two clusters are likely to be gravitationally bound in a pre-merger phase, and that CIZAJ1824 is moving toward RXCJ1825. Conclusions. Our results corroborate a picture where the Lyra region is the place of a very complex scenario of cluster assembly.