Using the 135 s cadence of the photospheric vector data provided by the Helioseismic and Magnetic Imager telescope on board the Solar Dynamic Observatory, we examined the time evolution of magnetic helicity fluxes across the photosphere during 16 flares with the energy class lower than M5.0. During the flare, in four out of 16 events, we found impulsive changes in the helicity fluxes. This indicates that even the flare with less energy could be associated with anomalistic transportation of the magnetic helicity across the photosphere. Accompanying the impulsive helicity fluxes, the poynting fluxes across the photosphere evolved from positive to negative. As such, the transportations of magnetic energy across the photosphere were toward the solar interior during these flares. In each of the four events, the impulsive change in the helicity flux was always mainly contributed by an abrupt change in the horizontal velocity field on a sunspot located near the flaring polarity inversion line. The velocity field on each sunspot shows either an obvious vortex pattern or a shearing pattern relative to the magnetic polarity, which tended to relax the magnetic twist or shear in the corona. During these flares, an abrupt change in the Lorentz force acting on these sunspots was found. The rotational motions and shearing motions of these sunspots always had the same directions with the resultant Lorentz forces. These results support the view that the impulsive helicity transportation during the flare could be driven by the change in the Lorentz force applied on the photosphere.