Here's something I saw with the LHFDMY/HDYLFM. First off, both contain the same letters (obviously), but the order of the letters in the second phrase is not random. When comparing the phrases as a whole (LHFDMYHDYLFM), starting at L in the second phrase, the distance between the two same letters is decreasing. L is 9 letters away from it's partner, F is 8 letters away, M is 7 letters, H is 5, & Y is 3. 4 & 6 are excluded. Now, this isn't all. Start off in the second phrase. Hop from each letter in the order of the first phrase. This works best if you draw it on paper. After you're done, you'll see it makes a consistent pattern. L to H, then back to F. F is to the right of L. Hop to D. D is to the right of H. Hop to M. M is right beside F. Hop to Y, competing the sequence. Y is right beside D. Now, whether any information can be gathered from this, I'm not completely sure. I am just showing that the second phrase is not arranged randomly and does, in fact, share a pattern with the first.
EDIT: Didn't play the Six Books game. Didn't realize that's how we got the second phrase. Whoops.