* Dreamliners grounded while battery issues investigated * LAN source says awaiting US regulator decision By Fabian Cambero SANTIAGO, Feb 26 LAN has not set a date to start flying its Boeing 787 Dreamliners again, a company source told Reuters on Tuesday, after a local newspaper reported the Chilean airline would keep its three Dreamliners grounded until June 29. Regulators around the world last month joined the United States in grounding Boeing Co's 787 Dreamliner passenger jets after a series of battery-related problems. "We're awaiting the FAA's (U.S. Federal Aviation Administration) approval and that Boeing confirms that approval, so there's no date for operations to resume," the source said. Chile's Diario Financiero reported on Tuesday that LAN's Dreamliners would fly the Santiago-Lima-Los Angeles route again as of June 30. LAN, which last year took over Brazilian rival TAM to form the regional LATAM Airlines Group, has not commented about the Dreamliner's battery problems. Shares in LAN were down 0.14 percent on Tuesday morning. Santiago's blue-chip IPSA stock index dipped 0.4 percent.