Short answers, pulled from the story.
Whitman and Lincoln never met and never spoke. Whitman estimated he saw Lincoln roughly twenty to thirty times between 1861 and 1865, sometimes at close quarters. William Barton found little evidence that Lincoln recognized him in those encounters.
Whitman wrote four major Lincoln elegies collected as 'Memories of President Lincoln' in Leaves of Grass: 'Hush'd Be the Camps To-Day' (1865), 'O Captain! My Captain!' (1865), 'When Lilacs Last in the Dooryard Bloom'd' (1865), and 'This Dust Was Once the Man' (1871). His final poem on the president, 'Abraham Lincoln, Born Feb. 12, 1809,' appeared in the New York Herald on the 12th of February 1888.
Whitman gave his Lincoln lecture series from 1879 to 1890, centering on the assassination and the years of the Civil War. Justin Kaplan counted Whitman's 1887 New York City lecture and its after-party as the closest Whitman came to social eminence on a large scale.
Whitman admired Lincoln deeply; his diary in October 1863 contains the line 'I love the President personally.' He also fashioned himself as Lincoln's 'interpreter,' partly to expand the readership of Leaves of Grass. The scholar William Pannapacker described the poetry in 2004 as 'a mixture of innovation and opportunism.'
Initial reviews of Drum-Taps and Sequel to Drum-Taps were mixed; Henry James accused Whitman of exploiting Lincoln's death, while William Dean Howells praised the work. 'O Captain! My Captain!' became Whitman's most popular poem in his lifetime. Twentieth-century critics shifted toward preferring 'When Lilacs Last in the Dooryard Bloom'd,' which came to be regarded as one of the most prominent poems of the Civil War era.
'O Captain! My Captain!' is the most popular of Whitman's Lincoln poems; the scholar William Pannapacker called it the most popular poem ever written on Lincoln. Critics have long preferred 'When Lilacs Last in the Dooryard Bloom'd' as Whitman's finest work in the cluster, and Helen Vendler judged Whitman's Lincoln poems to have proven to 'last the best' of all Lincoln poetry from the mid- to late-19th century.