I e-mailed LA Wildlife and Fisheries to see what the official rules were and this is what they had to say.
"Lead shot is legal for dove hunting except on some National Wildlife
Refuges, where steel-shot is required for all bird-hunting."
Good luck,
Larry A. Reynolds
Waterfowl Study Leader
Louisiana Dept. Wildlife and Fisheries
2000 Quail Drive
Baton Rouge, LA 70808
(225) 765-0456