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Born in Logan, Virginia, (now West Virginia), Walker graduated from the Virginia Military Institute (VMI) in 1845. He then became a civil engineer, and later, a farmer in Virginia.
When the Civil War began, Walker took command of the Purcell Artillery unit. After seeing action at First Manassas, Walker became the chief of artillery to General A.P. Hill. Lindsay Walker, as he was known, amassed a lengthy combat record, serving in every one of the Army of Northern Virginia's major battles except the Seven Days campaign (he was ill at the time). He commanded artillery of Hill's Light Division during the Battle of Harpers Ferry and the Battle of Antietam in the Maryland Campaign. When Powell Hill was promoted to corps command, Walker became the head of the Third Corps artillery. He commanded the corps' reserve artillery in the Battle of Gettysburg, directly commanding the battalions of Maj David G. McIntosh and Maj William J. Pegram. He had direct command of all the corps' artillery battalions thereafter, including in the Overland Campaign and the Siege of Petersburg. In all, Walker served in 63 battles and engagements and was never once wounded, despite being a large target at 6'4" tall and despite often serving in very hot fighting. Walker was promoted to brigadier general on February 18, 1865.
Post War career
After the war, Walker moved to Selma, Alabama, where he headed the Marine & Selma Railroad. He returned to Virginia in 1876 and became an engineer for the Richmond & Allegheny Railroad. As a civil engineer, Walker oversaw the construction of an addition to the Virginia State Penitentiary and the Texas State Capitol building.
Walker died in Fluvanna County, Virginia, and was buried in Richmond's famous Hollywood Cemetery.