As others have written, it would depend on the changes, if any. I don't want to see computerized drawings or higher odds. A successful business does need to be run by people who know how to run one, and the lottery is definitely a huge business. So I guess it depends on how "private" it really is.
One reason I look at privatization a bit negatively is from personal experience when I sold insurance to seniors. I saw the Good, the Bad and the Ugly. Recently many government run programs have had been leaning toward some form of privatization and they often hurt the general public more than help them, depending on your tax bracket and personal needs. The BIG difference is that the Lottery is a choice, so we can simply stop playing. Without getting into a long, boring discussion, one example of privatization is some of the new Medicare programs where private owners decide what to approve or not approve and design plans that are often deceptive. However, many offer excellent benefits. Another is private Health Insurance which has become a financial burden on the average breadwinner. People of means can afford the best Major Medical plans and benefit from the tax advantages of investing in a Health Savings Accounts. As many people know, Managed Care (like HMOs) has been around for many years and some plans are great, but a bad one can make decisions that hurt people (and kill them) when profit and greed come before people.
So am I just going off on a tangent here or can this be related to the Lottery? I know that, since it is a choice, any private company running a lottery will do its best to attract more players, right? The lottery isn't a life or death situation, although some people on this board might disagree!! So a private corporation would be different from a health care company that seeks out healthy people and punishes those who are ill. As long as the funds continue to be allocated to programs that help the citizens of the state, maybe it would not be such a bad idea.
In brief, I answered "Not sure."