No. Lottery tickets cannot be purchased at gas stations in Oahu, because the state of Hawaii doesn't have a lottery. They also do not participate in national lotteries like the Powerball or Mega Millions lotteries. No exact reason has been stated, but many believe that Hawaii doesn't have a lottery because the tourism industry is so strong in the state that the revenue from a lottery is not needed.
Hawaii is one of 7 U.S. states that don't have a lottery. The other states without lotteries are Alabama, Alaska, Mississippi, Nevada, Utah, and Wyoming. Alabama, Mississippi, and Utah don't have a lottery due to many in the states having strong religious convictions against gambling. In Nevada and Mississippi, the biggest reason there's no lottery is that a lottery would compete with the income of the casinos in those states. It's believed that Alaska and Wyoming don't have a lottery because of having lower populations and little interest among those who live there.