According to a Lehman Brothers Global Indices web page:

"Subject to the approval of the U.S. Bankruptcy Court and applicable regulators, and the closing of the transaction, as part of the proposed Barclays acquisition of Lehman Brothers' North American investment banking and capital markets operations, Lehman indices would be expected to become part of Barclays.

"Recognizing the industry significance of these indices, Barclays is committed to maintaining the family of Lehman indices and the associated index calculation, publication and analytical infrastructure and tools."

A market index is an asset of the company that owns it.  It can be sold to another company (who may decide to rename the index).  The owner of the index can get revenue from licensing the use of the index by mutual funds, exchange traded funds, and other types of investments designed to track the index.