The colors in the logo (grey to blue) represent the smooth transfer that Legato gives. And the "L" shows that Legato is the one that transfers the darker side to the lighter side. Which is why the L is in the middle of the two.
The "L" looks kind of like a "Z" - maybe if the L was lower case in the same font as the rest of the word. Also maybe try a little more texture or some extra "depth" to the sphere (or maybe even a different shape). Also try to incorporate the word "technologies" (but not "inc") - I think I want to have this present regardless of the design.
The L looks more like an L now, but still a little too similar to your previous entries.
The concept of having the first letter of "legato" in an "icon" has potential. I would like an iconic variation of the logo in addition to the full logo, but I don't really have an idea of what it would be. Maybe try a different shape, make it a little smaller (closer to the size of the text), and/or some kind of symbol(s) in the shape.
I'm trying to think of some ideas that would make it more "inconic" however, I think that it may get a little busy If I keep adding things. Do you think that maybe a swoop of some sort from the bottom of the L would work?
Heres one with the swoop. Not sure, that this is the way you are going though. I'm going to try a few other things with the bubble. Just wanted to give you anther view with this.
Here is a variation to the L before. I tried some lowercase L's and they looked more like 1's. If you would like me to add in the full word "Legato" after the logo I can do that as well, rather than cutting it off.