It has been known for a long time that a large fraction of disc galaxies are lopsided. We simulate three different mechanisms that can induce lopsidedness: flyby interactions, gas accretion from cosmological filaments and ram pressure from the intergalactic medium. Comparing the morphologies, HI spectrum, kinematics and m=1 Fourier components, we find that all of these mechanisms can induce lopsidedness in galaxies, although in different degrees and with observable consequences. The timescale over which lopsidedness persists suggests that flybys can contribute to ~20 per cent of lopsided galaxies. We focus our detailed comparison on the case of NGC 891, a lopsided, edge-on galaxy with a nearby companion (UGC 1807). We find that the main properties of NGC 891 (morphology, HI spectrum, rotation curve, existence of a gaseous filament pointing towards UGC 1807) favour a flyby event for the origin of lopsidedness in this galaxy.