I promote bingo sites and one lottery sites and I've found that offline marketing doesn't convert well. Unless you try to partner. For example I've partnered with an offline bingo hall they promote my site as an affiliate. My approach to the offline bingo hall is hey if you're going to lose your offline bingo players online might as well get a piece of the action. This is very tough and most turned me down. You might try the same approach for your lottery site. Also look at other sites lottery players would enjoy. Bingo players convert well to lottery sites. As do Keno, Pull-tab, slot players since the demographics are similar. Check out www.bingoa2z.com it is a good bingo network of several bingo sites that offer bingo, keno, slots. I do affiliate management work for them so let me know if you have any questions but try the cross-marketing approach. Also try to advertise on bingo portals and directories, there are many good ones out there.
Stefani - most things being peddled via spam is junk but there are a lot of legitimate well-run lottery and other gaming sites and they are not scams. So if you get spam on lottery, web design, logos, rx, etc. they are all the same it's not just because it's lottery.
One thing clotters make sure it's a legitimate lottery site not one of these international lottery sites those are scams!