Have you ever won the lottery without going to Oasis Landing?

It is possible, but the odds of winning the top prizes like §1,000,000 are extremely low, with a slight bonus given for having the Lucky trait. The odds of winning smaller amounts are greater. Your sim may have to purchase many thousands of tickets before they see a huge jackpot, if they ever do.

Or of course they may win on the first try, anything is possible. But without cheating around with the tuning files, I wouldn't base my storyline on that possibility until it happens. :)