One of the Large Sky Area Multi-Object Spectroscopic Telescope (LAMOST) scientific requirements require the ability of the low resolution spectrograph(LRS) to measure velocities to a accuracy of 4km/s over the entire 5 degree field in 2 hours objects observation. This requirement results in the specification of image movement less than 0.6μm/hours (0.05pixl/hours corresponding to the science detector).There are 16 spectrographs for LAMOST telescope, so we expect the design aspects of the instrument directed towards achieving the stability goal. In this paper we present the last design aspects of the instrument which enable meeting the 4km/s requirement, and the recent test results of the LRS’s Stability Performance. The test results show that the stability performance of LAMOST-LRS can meet the the stability goal, the image shift along the direction of dispersion is not influenced by the external factors, and the image shift along vertical dispersion direction meet the technical requirements when the environmental temperature of the spectrograph room is in control.