won the first prize in a/the lottery

Well, if you know what lottery it was, you would probably use "the." So, for example, if the person you refer to won the Irish Hospitals' Sweepstakes, you would say: "Oh, did you hear? Johnny won the sweepstakes!"

Now, if the only thing that matters is the money involved, and no particular lottery is involved, you would use "a." So, for example: "Where did Johnny get all his money? Oh, he won a lottery."

Many thanks, Setanta.

If you say that Johnny won the sweepstakes, does it means he won the first
prize ?

Where I live, there are several prizes in the Sweep. So should I state the jackpot or first prize to distinguish it from the above prizes?

Sure, first prize, jackpot, whatever . . . the same conditions would apply. If the money is the issue, us "a," if the lottery or sweepstakes itself is the issue, use "the."

Many thanks, Setanta.