I ran into an old friend, who, believe it or not, had over 30 years (since 1977) of New York Lottery data...I asked him if I could play around with it and wanted to see if I could garner interest on a site, so I threw this together quickly on Drupal - so it's not perfect, and the design isn't great, but, I didn't want to waste my time with something that I wasn't positive would even have a crowd!
Hey mate, I went to adwords.google.com and used their keyword tool to see what people are searching for. Here's some top results:
ny lottery - 450,000 January searches
nys lottery - 110,000 January searches
pick lottery numbers - 18,100
lottery past numbers - 14,800
new york lottery results - 12,100
Other interesting results: ny lottery org (12,100), nyc lottery (9,900), new york lottery com (6,600), nyc numbers (3,600), www ny lottery org (2,400)... and finally ny winning lottery numbers (1,000 - first mention of winning in combination with the way I typed the words in).
So, yes, these terms are getting searched. A lot of people are looking for the newest numbers, so if you could automatically have those post up, that'd add value to your site. Now, the way you'll get traffic to this site I'm guessing is SEO - so start thinking about a domain and keywords you want to go after. Monetizing? Totally doable I'd imagine, but not sure how you'd go about it. Links to playing or buying lottery something-or-other online might be good. Maybe sit in a convenience store and ask everyone who buys a lottery ticket if you can talk to them for a couple minutes, and ask them like five questions about their interests.
Do people who play the NY lottery like horseracing? The Yankees? Hot dogs? Going to Miami? It seems to me like you could get traffic with some effort, and could monetize with some effort, but the effort thing is key here. You're going to have to mess around and experiment to figure out the monetization side, and going to have to spend some time getting pagerank and relevancy if you want high traffic. But - it seems doable, and I'm going to guess you could carve out a few hundred bucks a week without too much effort, which is pretty cool. Good luck with the endeavor.