In the US, it's internally consistent.
You didn't earn an inheritance either, but inherited income is taxed (it used to be taxed at a higher rate than earned income, not sure what the rates are now). Of, if you buy $100 of the latest digital currency and it skyrockets to $40,000/coin, you didn't really earn that, but it's taxed as a short term capital gains income (or, some other form of currency trading investment).
The lottery is consistent with gameshows in the US. Like, Who Wants to be a Millionaire is really who wants to be a $565,000-aire. The $64,000 Question is really the $38,280 question. That Price is Right new car is really The Price is Right cash-equivalent because nobody can afford to hand over $9,200 in tax for the new car on the spot.
Sadly, lottery winnings might be a greater distribution of wealth than typical CEO salary or corporate earnings at a company like Apple
Portions of every lottery ticket go directly to local services (usually schools, public works, roads), and then the winner pays a little less than 50% tax on the winnings, which goes into the typical tax system.