United States India PAC is one at least.
Founded in 2002, USINPAC has a successful track record of supporting and opposing legislation independently, as well as working with issue-based coalitions. USINPAC proudly serves as a resource for Congress, the White House and for Indian-Americans in the USA and abroad.
A quick look at their own site shows that the advocacy is not only directly concerning Indian people living in the U.S. but also support of India. There may be others and certainly there are individual lobbying efforts.
Note that this is difficult to search for if you use “Indian” because in the U.S. we (used to/still do) call our Native People Indians, and there is a federal Bureau of Indian Affairs that concerns itself with Native Americans, not people from India or their descendants.