Output of MATLAB's two-dimensional DWT function $\tt dwt2$
The confusion is natural as the notations and practice are misleading, and differ across the different works on 2D wavelets. 


First, the order of operations ("row then column" or "column then row") is important. In most cases (to the best of my knowledge), LH means low-pass on rows, then high-pass on columns (so, giving horizontal edges). But in some contexts, people use filtering tools on "columnized signals", so the first filter works on columns, then the image matrix is transposed, the second filter pass is applied, and the result is transposed back. 
Second, from an math operator point of view, LH(I) is more often understood as applying the high-pass first, then the low-pass, enhancing the confusion. 
Third, one may think about the active derivative: a vertical derivation yields the horizontal features.


In the following image, the rightmost letter seems to denote the first filtering operation:



while the opposite convention is used in second image:



This might stems from a cultural and technical background: does one read images left-right then top-bottom, or  top-bottom then left-right? 

The best is to test your implementation, look at the resulting images, and use a consistent notation.