LOS ANGELES — Teachers walked rainy picket lines Thursday at Los Angeles schools for a fourth day ahead of a new round of contract negotiations that a union leader said is unlikely to quickly end the walkout. “After 21 months of negotiations I think it would be an unrealistic expectation to say that this is going to be over after today because there are hard issues to work through,” said Alex Caputo-Pearl, president of United Teachers Los Angeles. The office of Mayor Eric Garcetti announced it would facilitate the latest talks at City Hall.