BOSTON — MOUNTING debts and urban woes are edging one of the most innovative theaters in the United States closer to an untimely finale.The theater narrowly averted insolvency a week ago with an anonymous $100,000 gift, but unless there is a major infusion of cash and a survival strategy - possibly an affiliation with another theater - the Los Angeles Theatre Center (LATC) will close its doors in downtown Los Angeles, unable to meet its payroll or trigger a cultural renaissance in the area. Over the last 10 years the Los Angeles Community Redevelopment Agency has supported the four-theater complex with nearly $27 million in funds. LATC was intended to become the main attraction in a new downtown cultural center filled with art galleries, restaurants, nightclubs, and condomiums. Innovative theater presentations at LATC, reflecting the Asian, Latino, and African-American cultures in Los Angeles, won drama awards and critical acclaim. But a combination of theater mismanagement, a failure to pay federal and state payroll taxes, the economic recession, and the city's inability to forge a business revival in the rundown, high-crime area around the theater, have brought on the crisis. William Bushnell, artistic director of LATC, also blamed the Los Angeles Times which refused to run ads for the theater until it paid $56,000 in bills. The theater needs to raise $500,000 by the end of the month. But that will only meet immediate bills. Early this month the city of Los Angeles bought the theater building for $5 million by paying off the private bondholders. The city also provided a final $750,000 to LATC for maintenance costs. A spokesman for the Los Angeles Department of Cultural Affairs said if LATC fails, the city will probably organize a consortium to continue offering theater to the public. Meanwhile the L. A. artistic community is rallying to help the theater. Recently the cast of "The Phantom of The Opera" gave a cabaret performance that raised $214,000. At a press conference it was announced that the National Endowment for the Arts had provided $75,000 for LATC's back payroll taxes. And the Center Theatre Group in Los Angeles had given $15,000 to help pay rent on a facility housing LATC's scenery.