First of all, we should tell you that scientists aren't even sure why a small leg length difference would cause low back pain...but it does! Maybe the angle of the pelvis gets tilted enough to change how the muscles of the spine work together. Given enough time the changes lead to low back pain.
Having said that, we can also tell you it's not clear why a thin shoe lift gives people relief from their pain...but it does! A recent study compared two groups of back pain patients who all had one leg mildly shorter than the other.
One group had a shoe insert inside the shoe of the shorter leg. The other (control) group did not have an insert to correct the length difference. The group with the shoe insert all reported less back pain. There was no change in pain or symptoms for the control group.