We performed spectroscopic observations of the small-separation lensed quasar SDSS J1001+5027 , whose images have an angular separation \theta = 2. ^ { \prime \prime } 86 , and placed constraints on the physical properties of gas clouds in the vicinity of the quasar ( i.e. , in the outflowing wind launched from the accretion disk ) . The two cylinders of sight to the two lensed images go through the same region of the outflowing wind and they become fully separated with no overlap at a very large distance from the source ( \sim 330 pc ) . We discovered a clear difference in the profile of the C IV broad absorption line ( BAL ) detected in the two lensed images in two observing epochs . Because the kinematic components in the BAL profile do not vary in concert , the observed variations can not be reproduced by a simple change of ionization state . If the variability is due to gas motion around the background source ( i.e. , the continuum source ) , the corresponding rotational velocity is v _ { rot } \geq 18 , 000 km s ^ { -1 } , and their distance from the source is r \leq 0.06 pc assuming Keplerian motion . Among three Mg II and three C IV NAL systems that we detected in the spectra , only the Mg II system at z _ { abs } = 0.8716 shows a hint of variability in its Mg I profile on a rest-frame time scale of \Delta t _ { rest } \leq 191 days and an obvious velocity shear between the sightlines whose physical separation is \sim 7 kpc . We interpret this as the result of motion of a cosmologically intervening absorber , perhaps located in a foreground galaxy .