But that's part of the equation, right? If I win the lottery, after taxes I'll get....
I imagine it varies from lottery to lottery and may also depend on whether you take most/all of the money up front or take payments over time. However, the lottery commission is going to send a big chunk of change directly to the IRS and another chunk of change to your state's taxing authority (unless you live in a state that has no personal income tax).
A lottery win is going to push you into the top tax bracket, which, on the federal level, is 37% on income in excess of $539,900 or $647,850 (depending on your filing status). In California, for example, it's 12.3% on income in excess of $625,370 or $1,250,739. Bottom line, if you're in California, you're netting just over 50% of your winnings, and there ain't no way around it.
The first thing to figure out is how much is being withheld, and it's probably not going to be everything you owe. Obviously on a lesser magnitude, but I won some money on a game show 20 years ago, and they sent 20% to the feds but nothing to the state. This is why you get a tax/wealth management attorney and a high-level investment advisor on board ASAP.
You can, of course, give a shload of your net winnings to charity and use that as a tax deduction, but it's still money out of pocket. It's just going to the charity(ies) instead of the government. Once you've dealt with the initial tax liability, you can set things up so that the tax liability on earnings on your investments is minimized, but the initial hit can't be avoided.