A New York judge on Thursday cleared the way for the state lottery to name an operator for a long-stalled casino at Aqueduct Racetrack by rejecting a lawsuit seeking to get the bidding process restarted once again. At a Thursday hearing, Supreme Court Judge Barry Kramer threw out a lawsuit filed by Aqueduct Entertainment Group challenging the lottery’s decision earlier this year to reject the group’s bid after the lottery determined that several members of the group would not be eligible to receive a license, according to lottery spokeswoman Jennifer Givner, who attended the hearing. “The court found that the lottery had a rational basis for its decision and that it was not arbitrary and capricious,” Givner said in an e-mail message. The ruling comes as an enormous relief to the New York racing industry, which has been beset by financial problems for nearly a decade and frustrated by the state’s inability to name an operator for the casino. First authorized in 2001, the Aqueduct casino is expected to be one of the highest-grossing properties on the East Coast, and its 4,500 slot machines will likely generate $60 million each year for the New York Racing Association and its horsemen. The lottery is expected to announce Aug. 3 whether it will accept a bid made by Genting New York, a Malaysian casino company, to operate the Aqueduct facility. Although three companies applied for the license when bidding was reopened earlier this year, the lottery disqualified two of the bids shortly after receiving them. “The lottery is pleased with Judge Kramer’s decision, which affirmed the fairness and thoroughness of the lottery’s licensing and evaluation process,” said Gordon Medenica, the lottery’s director, in a prepared statement. “We will continue to apply the same rigorous standards and discipline to the current selection process for an Aqueduct operator.” Gov. David Paterson has said that he will approve any recommendation made by the lottery, but the recommendation also will need the approval of the leaders of the state Senate and Assembly. If the recommendation is approved, the earliest a casino could be up and running would be mid-2011, according to officials.