I think you're on slightly different thread than we are.
We were saying that $5M is easy to turn into $10M, but $5 is impossible to turn into $10. We were referring to the fact that good investment vehicles are only available to people with large sums of money.
As a result, a poor person will be more inclined to blow the $5 on a lottery ticket because she has no investment options. It's still not a rational choice, but in her mind, she has nothing better to do with that $5 than take a chance at winning $10M. In her mind, that's how she gets to be a millionaire and no other way.
We weren't suggesting that a lottery winner will be a smart investor.