The relation between personal wealth and personal utility is a complicated one, so your observation obviously has some merit. Ad-hoc extreme example: if I owe someone ten billions by next week or they will kill me, and I have no hope of escaping or borrowing the money, spending all of my little money on a lottery is rational since nothing else has the sky-high potential ROI I need (my function here hovers around a flat zero utility, for up to 9999999999 money).

Is the situation of poor lottery players sufficiently similar? My guess tends towards 'no'. Yes, the poorer you are the harder it is for you to 'normally' raise yourself to a decent standard of living - but since lottery tickets usually have a fixed nationwide price (unlike other comfort goods like alcohol and drugs), there is also the matter that the poorer you are the bigger the sacrifice you are making to buy those tickets. And I think that the latter factor outweighs the former.

Also, keep in mind that if we're discussing what is rational for someone to do, observations to the effect that "but they don't think like that" are beside the point - if they hold wrong ideas because of their environment/education/whatever, they're still wrong ideas.