Levi, and later Barr's Light Artillery Battery, was initially known as the Virginia State Line Artillery. From my sources when they disbanded and reformed into Levi's Light Artillery Battery on April 01, 1863, and into Thomas' Legion, some of the soldiers formerly served in one of the regiments within Hay's Louisiana Brigade; aka, Louisiana Tigers. Hence, the name Louisiana Tigers was adopted. Another version: Hay's Louisiana Tigers and the Virginia State Line Artillery both served in the Army of Northern Virginia. When the Virginia State Line Artillery disbanded and reformed into Thomas' Legion as Levi's Light Artillery Battery, they liked the name Louisiana Tigers and adopted it. Regardless, Hay's Brigade has first right to the name. 

Brigadier General Harry Hays' Louisiana Brigade, known as the "Louisiana Tigers", charged across the rolling Culp Farm and struck the Union positions at the base of the hill. The nickname for Hays' men came from former members of the original Louisiana Tigers or Wheat's Battalion, raised in 1861 but disbanded after Major Robert Wheat's death. The remaining Tigers were transferred into the various regiments of Hays' command where the other Louisiana soldiers had taken a liking to the nickname and the fame attached to it.

Colonel Isaac Avery's North Carolina Brigade and Brigadier General Harry Hays' Louisiana Brigade, known as the "Louisiana Tigers", charged across the rolling Culp Farm and struck the Union positions at the base of the hill.

Louisiana Tigers at The Battle of Gettysburg