Legalizing sports betting has absolutely no impact on state lottery sales.
States often fear that sports gambling will cannibalize the tax revenue they get from lotteries, but a study of 18 states found the two are not substitutes. They appear to attract different types of consumers or fulfill different psychological needs, meaning state budgets don't suffer when betting is legalized.
Sports Betting, Lotteries, and State Revenues in the Post-PASPA Era
SSRN · 6294538
State lotteries are a staple of state revenue for the 45 states that run them and are an important part of state public finance. Following the repeal of the Professional and Amateur Sports Protection Act (PASPA), 38 states, plus Washington, DC, began operating legal sports betting markets. It is unclear whether sports betting and lottery demand are substitutes, complements, or unrelated goods, but if the introduction of sports betting displaces expenditures from state lotteries to support sports