She was born in Elmira, New York, and attended Wesleyan Female College (1850–51) and the Catholic Academy of the Sacred Heart in Cincinnati, Ohio, where her theatrical family had settled.

[1] An 1865 novel, Chateau Frissac: or, Home Scenes in France, "was written with the view of showing the evils resulting from the well-known French mariage de convenance"[2] Her 1866 story collection Olive Logan's New Christmas Story: John Morris's Money was reviewed as "not notably worse than most of the fiction of the day".

[3] Olive was influenced by Artemus Ward to take up public speaking where she spoke on social and political topics.

She corresponded for many periodicals and wrote, besides plays (including a metrical rendering of Coppée's La Pasant), a dramatization of Wilkie Collins's Armadale, and several books on theatrical matters, such as Before the Footlights and Behind the Scenes (1870).

Some of Logan's lectures were on woman suffrage; she spoke at the 1869 convention of the American Equal Rights Association and was a contributor to The Revolution.

Her younger sisters Alice (1844–1917), Grace, and Kate (1847–1872) also appeared on the stage; notably Alice and Grace performed in the American debut of Lydia Thompson, considered the first burlesque performance in America, at Wood's Museum in New York in September 1868;[6] the theater was owned by George Wood, Eliza's husband.

They had at least one son, John Douglass De Lisle, who was the US consul in Bristol, England when he died of a cold in 1890.