God can bless people however He choses. I do not believe that the money is received in an ill gotten manner because people are well aware of the chances of winning before they play the lottery. However, If a Christian is putting their faith in the lottery to provide rather than God, THAT is a problem.
My thoughts concerning God giving large sums of money to Christians are this: God can do this in whatever way He wants; BUT, since God is omniscient (perceives all things) and knows what will come in the future, He also knows what will happen to that person who receives a large sum of money and the end result of an abundance thereof.
With a huge amount of money, also come a huge possibility that it will destroy a person and their relationship with the LORD. Having accumulated so much wealth can easily lead a person's heart away from God. That person may start putting their faith into money or they may become proud, greedy or take on multiple characteristics that are clearly spoken against in the bible.
People can say all they want about what they would do if they all of a sudden gained a lumpsum of money such as: giving to charity, helping the needy, improving their community..... but the truth is; only God knows exactly what that money would do to that person.
I cannot not say one way or the other that a lottery win does or does not come from God; but I can say this: if it is, He will make sure it gets into the right hands, for the right reasons, at the right time.
Seek first the kingdom of God and His righteousness.