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My initial, immediate, off-the-cuff answer would be, "Well, no. Christians shouldn't play the lottery." You know why? It's hard. I guess the lottery is gambling, or it's coveting something that's not yours, but if you even back up and just think about it a little bit, as we work our way through the book of Luke for instance, there's so much there about stewardship, how to handle finances, which we know all things belong to God.
Is it wise to do that? We know that the lottery is set up on a losing ... Gambling's a losing proposition, and so from a common sense perspective, it just doesn't make sense to invest in something where you know you're probably going to lose. So, in that sense, playing the lottery as a Christian just doesn't make sense. It's not good stewardship of what God has provided.
I think the question is even deeper. Why would a Christian want to do the lottery? I think that's a even more pertinent question because ... Why is it that I want to play the lottery as a Christian? Is it I hope that I can hit it big, therefore all of my needs are going to be taken care of where God has already promised, my God shall supply all of your need according to his riches and glory by Christ Jesus, but when he doesn't, then I can hit the lottery. I just think it's against who we say we are as believers. I trust in God. I don't have to trust in a lottery to fulfill my needs or to make me happy.