A sales tax on groceries or a sin tax on cigarettes may be regressive because poor people spend a larger portion of their income on groceries and cigarettes, true.
The lottery, however, is worse. It is actively advertising to these people, encouraging them to have hopes and dreams about a way out of their situation, but instead it just kicks them while they're down. And it's not just some soulless corporate entity doing this, no: it's the same government which purports to care about their plight, not just exploiting them but encouraging them to passively hope for unearned success, instead of pursuing goals as an independent actor or something which might actually improve their lot.
"Hey, you never know!" is a dystopian lie, a few increments worse than "A new life awaits you in the off-world colonies! A chance to begin again in a golden land of opportunity and adventure!"