Is it not grotesque to give a random person 1.2 billion dollars in a lottery?

First of all, they are not getting $1.2B. The lump sum cash value is $551.7M. The usually reported jackpots are presented in terms of the value of a 30 year annuity.

Second, those winnings are before taxes. After taxes, depending on the state, the person will walk away with $280m-350m.

Now, sure, that is still an absurd amount, but still like 1/4th the stated jackpot.