* Refugee will need months of treatment, doctor says * 2014 UN appeal is only 14 percent funded - UN official * Refugee crisis is challenge to Leba**n's new government By Yara Abi Nader BEIRUT, April 2 (Reuters) - A U.N. official said a Syrian refugee in Leba**n who doused herself with petrol and set herself alight after her aid was cut was a victim of a lack of funding for the world body's work. The millionth Syrian refugee will register in Leba**n on Thursday, the U.N. refugee agency says, adding to the strain on a county of only 4 million which is struggling to stop the war from flooding into its territory. Mariam al-Khawli, who fled Syria with her husband and four children two years ago, set herself on fire last week in frustration at living without the food and cash lifeline provided by the United Nations since August. Her story has become well k**wn over the past days, after appearing in news outlets in Leba**n.