In this article we show results on cavity-free lasing in nitrogen filaments using our 3D, time-dependent Maxwell-Bloch code, Dagon. This code was previously used to model plasma-based soft X-ray lasers and it has been adapted to model lasing in nitrogen plasma filaments. In order to assess the predictive capabilities of the code, we have conducted several benchmarks against experimental and 1D modelling results. Afterwards, we study the amplification of an externally seeded UV beam in nitrogen plasma filaments. Our results show that the phase of the amplified beam carries information about the temporal dynamics of amplification and collisional processes inside the plasma, along with information about the spatial structure of the amplified beam and the active region of the filament. We thus conclude that measuring the phase of an UV probe beam, in combination with 3D Maxwell-Bloch modelling, might be an excellent method for diagnosing electron density value and gradients, mean ionization, density of N2+ ions and the magnitude of collisional processes inside these filaments.