Previously unremarkable, the extragalactic radio source GB 1310+487 showed a gamma-ray flare on 2009 November 18, reaching a daily flux of ~10^-6 photons/cm^2/s at energies E>100 MeV and becoming one of the brightest GeV sources for about two weeks. Its optical spectrum is not typical for a blazar, instead, it resembles those of narrow emission-line galaxies. We investigate changes of the object's radio-to-GeV spectral energy distribution (SED) during and after the prominent GeV flare with the aim to determine the nature of the object and constrain the origin of the variable high-energy emission. The data collected by the Fermi and AGILE satellites at gamma-ray energies, Swift at X-ray and ultraviolet, Kanata, NOT, and Keck telescopes at optical, OAGH and WISE at infrared, and IRAM 30m, OVRO 40m, Effelsberg 100m, RATAN-600, and VLBA at radio, are analysed together to trace the SED evolution on timescales of months. The gamma-ray/radio-loud narrow-line active galactic nucleus (AGN) is located at redshift z=0.638. It is shining through an unrelated foreground galaxy at z=0.500. The AGN light is likely amplified by a factor of a few because of gravitational lensing. The AGN SED shows a two-humped structure typical of blazars and gamma-ray-loud NLSy1 galaxies, with the high-energy (inverse-Compton) emission dominating by more than an order of magnitude over the low-energy (synchrotron) emission during gamma-ray flares. The difference between the two SED humps is smaller during the low-activity state. Fermi observations reveal a strong correlation between the gamma-ray flux and spectral index, with the hardest spectrum observed during the brightest gamma-ray state. If the gamma-ray flux is a mixture of synchrotron self-Compton (SSC) and external Compton (EC) emission, the observed GeV spectral variability may result from varying relative contributions of these two emission components.< Réduire