The mechanisms producing fast variability of the γ-ray emission in active galactic nuclei (AGNs) are under debate. The MAGIC telescopes detected a fast, very-high-energy (VHE, E > 100 GeV) γ-ray flare from BL Lacertae on 2015 June 15. The flare had a maximum flux of (1.5 ± 0.3) × 10-10 photons cm-2 s-1 and halving time of 26 ± 8 min. The MAGIC observations were triggered by a high state in the optical and high-energy (HE, E > 100 MeV) γ-ray bands. In this paper we present the MAGIC VHE γ-ray data together with multi-wavelength data from radio, optical, X-rays, and HE γ rays from 2015 May 1 to July 31. Well-sampled multi-wavelength data allow us to study the variability in detail and compare it to the other epochs when fast, VHE γ-ray flares have been detected from this source. Interestingly, we find that the behaviour in radio, optical, X-rays, and HE γ-rays is very similar to two other observed VHE γ-ray flares. In particular, also during this flare there was an indication of rotation of the optical polarization angle and of activity at the 43 GHz core. These repeating patterns indicate a connection between the three events. We also test modelling of the spectral energy distribution based on constraints from the light curves and VLBA observations, with two different geometrical setups of two-zone inverse Compton models. In addition we model the γ-ray data with the star-jet interaction model. We find that all of the tested emission models are compatible with the fast VHE γ-ray flare, but all have some tension with the multi-wavelength observations. MAGIC and multiwavelength data are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/623/A175