Yes, the Index of Louisiana Deaths is available in several places for deaths that took place over 50 years ago, but Louisiana does not make the certificates themselves available on-line. You can't even get the certificates except through the Louisiana State Archives and they provide only certified copies for $5.00 each. You can go in person and copy them for about $.50 (someone correct me if I'm wrong on cost), but by mail it cost you $5 each. However, Texas death certificate images are available for many Texas deaths on the LDS Records Search pilot for free.
Anna