If you look at the example of https://www.mathworks.com/help/vision/ref/extractlbpfeatures.html#buumhtk-7 then you can see that the histogram for the rotated bricks is not exactly the same as the historgram for the unrotated bricks. That tells you that LBP is not rotation invariant.
The point is that LBP of the rotated version will be closer to the original than LBP of something that has a different texture. Not exactly the same as it would be if the measure was invariant, but close.
