The intriguing binary LS V + 22 25 (LB-1) drew much attention after being claimed to be a 79-day binary comprising a B-type star orbiting a ~70Ms black hole - the most massive stellar black hole reported to date. Subsequent studies showed that evidence for such a large companion mass is lacking. Recent analyses implied that the primary star is a stripped, He-rich star with peculiar sub-solar abundances of heavy elements such as Mg and Fe. However, the nature of the secondary, which was proposed to be a black hole, a neutron star, or a main sequence star, remains unknown. Relying on 26 newly acquired spectroscopic observations secured with the HERMES and FEROS spectrographs, we perform an orbital analysis and spectral disentangling of LB-1 to elucidate the nature of the system. We find that LB-1 contains two non-degenerate stars. The "hidden" secondary is a rapidly rotating (vsini ~ 300 km/s) B3 V star with a decretion disk - a Be star. The properties of the primary match those predicted for stripped stars: it is He- and N-rich and portrays significant Balmer-line emission, presumably stemming from its wind. Adopting a light contribution in the optical of 55% for the stripped primary, the abundances of heavy elements are found to be solar. With the derived value of K2 = 11.2 +- 1.0 km/s and by calibrating the mass of the B3 Ve secondary to M2 = 7 +- 2Ms, we derive an orbital mass for the stripped primary of M1 = 1.5 +- 0.4Ms. The orbital inclination of 39 +- 4deg implies a near-critical rotation for the Be secondary Veq ~ 470 km/s. Hence, LB-1 does not contain a compact object. Instead, it is a rare Be binary system consisting of a stripped donor star and a Be mass accretor rotating at near its critical velocity. This system is a clear example that binary interactions play a decisive role in the production of rapid stellar rotators and Be stars.