* Refugee will need months of treatment, doctor says
* 2014 UN appeal is only 14 percent funded - UN official
* Refugee crisis is challenge to Lebanon's new government
By Yara Abi Nader
BEIRUT, April 2 (Reuters) - A U.N. official said a Syrian refugee in Lebanon 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 Lebanon 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 doctor, Gabriel al-Sabeh, said 70 percent of Khawli's body was now covered in burns and that she could remain in hospital for months if she survives.
Khawli husband is unable to work due to a lung abscess and three of her children have a blood condition and they had relied on the aid. Her story has become well known over the past days, after appearing in news outlets in Lebanon.
"We really got hungry ... but they burned my heart before they burned my body. They burned my heart from the inside," she told Reuters of how she regarded the U.N. cutback.
Ninette Kelley, regional representative for Lebanon at the Office of the United Nations High Commissioner for Refugees, said: "Right now we have close to 1 million refugees and we are able to do a lot with the funding we receive but we simply do not have enough."
She said Khawli's case was "a very sorrowful reflection of the enormous desperation and need of the refugee community and it is also a telling reminder of the consequences of the Syrian emergency and the unfolding crisis here in Lebanon".
She said the agency had been in touch with Khawli's family "for many, many months", but gave no details of why the funds were cut or how many other families might have been affected.
U.N. aid teams in Lebanon give aid to the most vulnerable first and makes regular checks on families who are not covered, Kelley said.
Last month, Lebanon's foreign minister said the crisis was "threatening the existence of Lebanon", still recovering from its own bloody 15-year civil war that ended in 1990.
Syrian beggars now walk the streets of Beirut and informal tented settlements have sprung up around the country.
Syrian rebels and their Lebanese allies fight openly with the army and militants from the Lebanese Hezbollah militia, which supports Syrian President Bashar al-Assad in a war now in its fourth year.
The United Nations says 2.5 million Syria refugees have registered in total, more than 10 percent of Syria's population. Lebanon holds the largest number but Syrians have also fled to Turkey, Jordan, Iraq, Egypt and elsewhere.
A U.N. appeal for $1.7 billion in 2014 to help the refugees is only 14 percent funded, Kelley said.
The mounting cost of the refugee crisis is also a major challenge for Lebanon's new government, which has to deal with strained public infrastructure as the Syrians seek housing, food, and healthcare at a time of economic slowdown in Lebanon.
Showing how the conflict is spilling over, two missiles on Wednesday hit Al-Labwa, a Shi'ite town in Lebanon that has been hit before by Sunni militants in retaliation for Shi'ite Hezbollah's role in Syria.
The strikes are the latest in a series of missile attacks, bomb explosions and gun fights that have grown as the Syria conflict has become increasingly sectarian. (Writing by Oliver Holmes; Editing by Alison Williams)
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