Well they can and most likely would be able to sue you the individual, However since the trust would not own the property or say a vehicle then the trust on paper owns the lottery winnings although you in reality own the trust, the trust can not be sued if the accident happens on your property they would have to sue you and not the trust. There are other ways of protecting your cash as well that involve things like trusts and corporations and the like. It's a matter of legal definitions and not real world definitions. How things are worded, placed, accounted for effect just how much people can try to screw you over. Claiming a lottery prize as an individual leaves others too many ways to get at your money.
Thing is I've seen this principle explained on some other sites much better than I can. If you have a huge lottery win get a very good attorney before you claim anything, a tax advisor as well. Do not claim it in your own name.
If you are sharing with family a trust is very important as well. Especially if you are not splitting things down the middle. Anyone you are gonna share with needs to be set before you claim the prize regardless or you and they will pay more taxes.
As I've said before most people are not ready to recieve a huge lottery win, discussions like this help in the event these people who are not ready do win. So they don't blow it big time.
Best advice for anyone winning is get a lawyers and an advisor, form a trust and set amounts for others up front, tell them that's it, Decide exactly what you want to do the first 2 years with the money, Blow 10% off the top on rediculas things (no helping people, no charities) blow that 10% stupidly so that when that 10% is gone you will hate spending money.
after you get the new house and car etc etc go on some trips and just let the rest of the money sit there for a couple years until you get your head around being very wealthy.
But before the lottery win I would suggest that people do what I did a few posts back. Seriously list off everything you are planning to do with a lottery win and include what that would cost. Then add it all up and see how big of a lottery win it would take to achive those things and how much you would have left over.
Be very specific and on the high side on how much things would cost. Mine came it at a little over 11 Million dollars and I'm not planning on helping anyone but my own family. People talking about helping cousins and such... well they are gonna need a huge huge win if they really examine the costs of things.