People should have to be over 18 to buy a lottery ticket for the simple facts that teenagers do not have any respect for money, and will blow all the winnings in a few years just as many have done before them. Also since gambling is an addiction, you would not want to start children out early and possibly addict them to such a game.
Yes, people should have to be 18 to buy lottery tickets because gambling can be addictive, even for those over 18. Persons under 18 have not yet developed the ability to completely say no to compulsion, so the compulsion to buy many lottery tickets would be even worse for them.
Here's the thing if I wanted to when I was under 18 I could have gotten a friend above 18 to buy the tickets for using the money I gave him. So why wouldn't we just make it available to all people??? What do lottery revenues benefit?
Lottery proceeds benefit different programs in different jurisdictions. In many cases lottery profits are combined with tax and other revenues in a government's general fund. In other cases lottery proceeds are dedicated to a wide range of causes, including education, economic development, the environment, programs for senior citizens, health care, sports facilities, capital construction projects, cultural activities, tax relief, and others. Now if you could buy the tickets at any age the number would in theory increase even more allowing great causes to have more funding.