I can't complain about how Team Rocket goes about getting Lugia, but it feels like you're throwing Lugia in there just because you can. I mean, the game-versions of TR is cool and calculating; they always do their homework and are generally well prepared for anything that comes their way, yet you have them controlling Lugia just because it is 'around'? You're making it sound like they are going out into a paddock, flipping a switch and seeing what happens, only to never use the machine again.
I don't think I'm getting my point across very well because everything is starting to sound like gibberish to me D:
Basically, TR would be much better prepared before embarking on such a project. Back-up machines stationed all around the region to take advantage of all the ledgendaries hiding in all sorts of nooks and crannies. They'd have tons of files and status reports spanning over years, yet, from the way you have written it, it sounds like they've barely invested energy into it or prepared for longer than a month.
Don't pay attention to my indecipherable ramblings - I've had a long day D:
I'd like to quote something that I stated in my post further up this page.
Their goals? Lots of money. Their desire? Even more money. Why do they do the things they do? Money, money, money.
If you do have Team Rocket attempting to take over the world, that would be pretty OOC and go against all sorts of canon.