I was amused to see that the Conservative former Prime Minister John Major is being credited by some for Britain's medal haul at the Rio Olympics because it was his Government which introduced the National Lottery in 1994, and ensured that a large portion of the revenue from it was spent on improving facilities and coaching for elite sports, especially in multi-medal events such as cycling and swimming, a policy others have somewhat outlandishly compared to the State sponsoring of Eastern bloc athletes in the 70's and 80's.
There are three basic arguments against the National Lottery.
The first is that it's a tax on the poor, because poorer people will spend more on tickets in the hope of becoming a millionaire, a sort of low cost, no risk get rich quick scheme, albeit one with little chance of paying off. I'm not sure however that many people, if any, become addicted to buying lottery tickets, as opposed to gambling in high street bookmaking shops or online.
The second is that by generating not just cash for its operators but a sense of excitement around the draw amongst players, it serves as a distraction from the social ills that people would otherwise focus on (the same argument has also been made about mass spectator sports like football). George Orwell in his novel Nineteen Eighty-Four even predicted it when he wrote, "The Lottery, with its weekly pay-out of enormous prizes, was the one public event to which the proles paid serious attention." The problem with this argument is that people can play and be excited about the Lottery and be aware of and angry about the cracks which the cash from it helps to paper over (in the case of sport, it can even generate a sense of solidarity and become a focus for opposition). It also assumes that if such "distractions" were somehow abolished, people would almost automatically switch their attention to resisting our rulers' latest dastardly plans.
The third, and strongest, argument is that Lottery cash substitutes for public spending and lets the Government off the hook in its social responsibilities. If Lottery funding ceased, it's doubtful that public spending would increase to match the shortfall, but while it's clearly a problem if schools, hospitals or homelessness charities become dependent on grants, it's much less of one if the British Olympic track cycling team does. And, unlike your taxes, if you don't agree with what Lottery money is spent on, there's a simple solution: don't buy a ticket.