Then the lottery is a kind of fraud, because the winnings are taken by people at the expense of other people.
No, because the payments will not be exclusively from new investors (which don't exist in a lottery since it is gambling). If you are going create this kind of false equivalence then you can say that any type of gambling is a ponzi scheme.
(And if you want to extrapolate it further, any
company is a ponzi scheme)
I'll tell you more - every bank is a Ponzi scheme, every social and pension program. Just think over it.