I think lottery comparisons are a bit flawed, but they can be saved by turning them around. A lottery, by definition, means each person is trying to get a single sequence to win, even if the actual sequence isn't known at the time. More aptly, if you consider the number of tickets sold, what are the odds of the lottery picking the numbers of one of them. It's slightly reformulated, but more accurate, I think.
For example, say the lottery is one where three numbers are picked from a pool of 100. There should be 970,200 combinations (assuming the order didn't matter). So, if you buy one ticket, you've got a 1 in 970,200 chance. If you buy 2, you have a 2 in 970,200 or 1 in 485,100 chance. But, you're still trying to get to one specific group of numbers. Evolution doesn't work that way. So, if 100,000 tickets are sold, what are the odds that the lottery will pick one of them?
This means, there are 100,000 possible ways to win, and 870,200 ways to not win. Which is much closer to how evolution works, especially if the lootery continues, the jackpot raising, until someone wins eventually.