Do you believe that poor people are significantly more susceptible to triggering addictive behavior? I think a simpler explanation for why poor people play the lottery is that they see it as a way out of being poor.
That said, I don't think income level has anything to do with it. There are poorer people who shouldn't waste money to play the lottery or gamble in casinos, but do it anyway. There are also wealthier people who shouldn't waste money to play the markets, or other "casino/lottery for rich people" things, but do it anyway. It's just that our society is mostly oriented to treat the poorer people as compulsive gamblers -- which is treated as a moral failing -- and the wealthier people as "serial investors" or other terms which carry a more positive connotation.
https://www.theatlantic.com/business/archive/2013/11/your-br...