Did Serena really just get that lucky?

Yeah she got a little lucky, but Azarenka always gets tight when she is close to the finish line. I still remember the US open 2012 final where Azarenka couldn't serve out the match, and ended up losing the final to Serena.

She's had excellent teaching & coaching, plus, her Dad, Richard, managed her and Venus very closely. She knows very well that hard work is required to have a shot at success. I feel that the strength of a player's support group often goes underestimated. Serena has, IMHO, by far, the best serve in women's pro tennis. She can almost ace people at will!

So, no, it is not really luck, although there is always a bit of luck involved. You might say she is lucky to have had the background help available to her for so many years.

That's what make her a great champion. Even when she looks vulnerable or when her opponent who is seen as the underdog play well, she still wins.