Here are some things to think about...
When considering the reference to who got it: "It" is the most non-specific pronoun. "It" doesn't denote gender,number, or even if we mean person or object. This takes the value of human life almost entirely out of the equation or discussion.
Not using the word win demonstrates the irony of this entire story. The way we look at a lottery today is positive. (That in itself is an irony as everyone who doesn't win a cash prize is esentially a loser, those folks being the greater number) People used to cast lots. The person with the shortest straw or stick was 'it'. Under most circumstances, this was a negative thing for that one person. Everyone else then found themselves winners. That was the case in Shirley Jackson's The Lottery. I think we can all agree though that any member's life loss in a society is not a win.
In this story, it would really quite inappropriate to use the word "win" since the person who "wins" the lottery gets killed. So a few different words are used instead.
For example, after the drawing is conducted, the people are asking "who is it" or "who got it." Someone else says later on that they "hope it's not Nancy." They do not ask "who won?"
Of course, one of the major points of the story is to portary evil and horror as very normal things. However, I think it would be going too far to make it sound like someone wins when they are picked.