I think the "lucky" aspect comes with the fact that they were not able to create a consistent contender out of that. In their best 7 year stretch that included that 05' season, we saw only 3 90 win teams. Don't get me wrong, that's not bad, but when you think that those took place 7 years apart outside of 05', you get kind of a one-hit wonder team.
That team was fantastic and dominant, but I think management could've done a better job loading up the farm system a bit more to create a real dominant team of the 00s. I don't consider them a dominant team throughout the 00s.
Certainly that 05' team was not lucky. The fact that the stars aligned was not an accident. 99 wins is no joke no matter what. But at the end of the day, the 00s were not dominated by the Sox, whereas the next 8-10 years could be dominated by the Cubs.