When Annie Lennox was approached about writing the end title song for A Private War, Matthew Heineman’s searing biopic about war correspondent Marie Colvin, she hesitated because she hadn’t written new music in eight years. Instead Lennox, who won an Academy Award for best original song for “Into the West” from 2003’s Lord of the Rings: The Return of the King, has focused on improving women’s rights globally through her NGO, The Circle. However, she vowed “to try” to write a song because she had such respect for Colvin, who was killed in Syria in 2012 during an airstrike. The result is “Requiem for a Private War,” a spare, haunting, elegiac tribute to Colvin and a meditation on the horrors of war.