I'm afraid you're looking for logic where they may be none. My experience with multiFX units indicates that presets tend to be set up to give a selection of the most commonly used tones on the one hand and to showcase the units capabilities on the other. This generally results in a list with some basic tones near the top and progressively specialised tones near the bottom.
I've looked at the preset list you've linked up and I must say it isn't terribly helpful to the user, given how they leave it up to you to come up with preset names (which would somehow reflect what they sound like). Without the actual effect in hand, it's nigh impossible to even guess what the sound of each preset is, let alone what the organising principle may be (if any).
However, I understand your problem and there are several solutions to it.
The first thing you should do is go down the list of presets and decide which ones you like. Write a name or description in the preset list for each of them, so you know where they are (you can skip those presets you don't like - a blank in the list will indicate that there's nothing worthwhile there).
The second step is deciding whether you will mostly be playing single presets, or switching between them.
In the first case, it's fairly simple to get playing. Simply locate the relevant preset on your annotated list and play. After a while, you'll remember where each of your most commonly used presets is located and won't have to look them up any more.
However, easy preset switching is what we get multiFX units for in the first place and it would be a shame not to use this feature. For that, however, you'll need to shuffle the list a bit.
The bad news is that since the LX1 is such a basic unit, doing this is going to require some work. Storing presets to different locations than originally is easy enough, however, you will be overwriting the preset in that location.
Now, this may not be a problem - if you have a longer (4 or 5 presets, say) portion of the factory list where there's nothing of interest to you - it's fair game to be overwritten with a logically organised collection of your preferred presets. You can always restore the factory presets (all of them or one at a time) at a later date.
If you want a different preset in a given location, but don't want to lose the preset that's already there, I'm afraid you'll have to do it by hand. This involves writing down the settings for the preset to be overwritten on a piece of paper, overwriting the preset as before and then finally setting up the preset that you copied to the new location with the setting you wrote down. Consider it a semi-manual preset swap.
Needless to say, you'll have to write out a new preset list if you changed preset locations - you can print out the relevant page from the PDF you linked up for this purpose.
A final word on organising presets for easy swapping in an up-down switching situation: since you'll be restricted to moving Up or Down one preset per pedal press, it helps to organise presets for easy accessibility in a playing situation. For a lot of songs that I personally play, I found a chain of: clean sound - OD rhythm - solo/lead sound to work best. Thus for the body of the song I'd be switching between clean and OD by a single tap of the Up or Down pedal and when it came time to play leads or solos, a single tap of the Up pedal would get me from the OD rhythm sound I'd usually be playing prior to the lead sound for the solo.
You might find this organising principle of threes helpful if you choose to shuffle presets around.