I downloaded the demo yesterday night (about midnight), and decided to try a few turns. When I stopped, it was 4:00... so I guess it's at least a partial success
It's not completely successful for me, though, because I had some technical problems. The game seems awfully slow for such a simple program (my computer isn't exactly state of the art, but it does run "big" games from a few years ago like Morrowind and Neverwinter Nights - actually it was built with Morrowind in mind, and if LOL is more resource-intensive than Morrowind I think there's a problem); often response is sluggish, and that's too bad.
Also, from time to time the game will iconize and bring me back to the desktop, with no intervention from me. This might be a strange interaction with my antivirus, but it's still annoying.
At the moment, unfortunately, these problems are probably enough to stop me from buying the game - such a "light play" game needs to be responsive.
Other than that - the AI is rather weak, because it never gave me any kind of trouble and I'm not exactly a god of this kind of games (in all my games, the "flood them with the cheap units" strategy worked pretty well)... I guess I'd have to get trounced in multiplayer.
Oh, and for the record, even though I'm a past customer of Shrapnel (Dominions and Space Empires), I want to say I heard about LOL in a French mag, PC4War, in a preview by PDF - another die-hard Dominions fan. It's not an online mag, though, so it probably doesn't have to be included in the list of reviews/previews.