Try a Google Search with Keyword Lottery of the Newsgroup Alt.Sex.Stories.

There is some debate about who is the author and around 46 chapters of the story itself. Night Wind seems to have the strongest claim.

There is also another story called The Lottery in 80 parts by Dark Vision at

http://www.asstr.org/files/Authors/Darkvision/

I've only just found this one, following my own advice to always check ASSTR.