FROM OUR REPORTERS BARBARA ROSS AND TRACY CONNORWhen the cops raided Zuccotti Park, lawyers for Occupy Wall Street immediately woke up a judge with a civil liberties background and asked for help. Manhattan Supreme Court Justice Lucy Billings signed an early-morning order temporarily barring cops from keeping protesters and tents out of Zuccotti Park.But within hours, she was off the case as court administrators prepared to randomly choose a new judge — and excluded Billings’ name from the list of candidates.Billings’ biography notes that before she became a judge in 1997, she spent 25 years as a lawyer for the American Civil Liberties Union. “I have devoted my career to public service, especially the disadvantaged in desperate circumstances,” she wrote in a 2007 pre-election statement.Lawyers for Occupy Wall Street phoned Billings after cops moved into Zuccotti Park early Tuesday, evicted the protesters and got rid of their tents and other camp equipment. Asked why they called her first, protest lawyer Daniel Alterman wouldn’t say, remarking that he’s not a “gossip guy.” The lawyers also called an emergency hotline set up to assign judges to after-hours casesA staffer told them that since Billings had already been contacted, she should handle the Zuccotti matter. He said Billings came to the lawyers and at 6:30 a.m. signed an order declaring cops cannot evict protesters who aren’t breaking the law or stop protesters from entering with tents. Billings’ involvement will be short-lived.At 11:30 a.m., court officials were scheduled to use a computer program to pick a new judge for an afternoon hearing on the restraining order — the proceeding that will determine if the tents can be erected again. Billings’ name will not be included because she usually handles real estate cases, court officials said.