There are no specific books published about the 2nd Louisiana Cavalry. There is information available, but it is scattered throughout the literature.
The Official Records (Armies & Navies) have numerous mentions
Christopher Pena - Scarred by War
Donald Frasier - Fire in the Cane Field (plus the 3 further books planned in Dr. Frasier's "Louisiana Quadrille")
John Winter - The Civil War in Louisiana
Arthur Bergeron, Jr. - Guide to Louisiana Confederate Military Units
David Edmonds - Yankee Autumn in Acadiana
Gary Joiner (2 Books) - One Damn Blunder Beginning to End; Through the Howling Wilderness
Ludwell Johnson - The Red River Campaign
Morris Raphael - The Battle in the Bayou Country
William Riley Brooksher - War Along the Bayous
Thomas Ayres - Dark and Bloody Ground
And - many more, including numerous history journals.
Sorry I can't give you a more direct and specific answer. Although the above are somewhat repetitive relative to the 2nd LC, they all contribute to building a story about the unit of our ancestors.
Hope this helps in some way.
Very best
Don Parker