not sure if this will help but here is a paper titled Rainmakers: Why Bad Weather Means Good Productivity that might shed light on statistical methods to quantify weather effects,
A working paper that is methodologically very strong would be http://repub.eur.nl/pub/6890/ERS%202005%20045%20MKT.pdf . This is probably only helpful for the body of your question, not for the title. Unless you hand out lottery tickets in return for participation of course.
What an interesting topic! IOne issue with the Bruyneel et al. article is that the sunlight variable is treated as normally distributed, which it is in a statistical sense. But is that what we mean by 'a sunny day?' There's 'a sunny day,' and we're cheerful, and so we don't buy a lottery ticket because we're outside playing with the puppy, and we don't pick up the phone and talk to the pollster. Or it's rainy, so we watch the telly, pick up a lottery ticket, and out of boredom talk to the pollster. You see what I mean? Maybe the best way to think about it is "a sunny day," "an OK day," "a dreary day" (-1, 0, +1).