Lakshadadweep Islands are far west India, in the Arabian Sea on the opposite side of the subcontinent from the Andaman and Nicobar Islands. They are, geologically, an extension of the Maldives. You can reach them via small plane or cruise boat from Kochi, but AFAIK independent travel is restricted and you have to sign on to a package.

Can't review the diving, but if you haven't already you might want to visit the Lakshadadweep Islands website.