"Little India" has been used to describe the area since the early 1980s.
Wikipedia: Murray Hill, Manhattan
Murray Hill is a neighborhood in the New York City borough of Manhattan. Around 1987 many promoters of the neighborhood and newer residents described the boundaries as within East 34th Street, East 42nd Street, Madison Avenue, and the East River; in 1999, Frank P. Vardy, the demographer for the City Planning Commission, said that the traditional boundary is within East 34th Street, East 40th Street, Madison Avenue, and Third Avenue. The neighborhood is part of Manhattan Community Board 6.
South of Murray Hill, blocks on Lexington Avenue around 28th Street are sometimes informally called “Curry Hill,” due to the current high concentration of Indian restaurants.
23 April 1995, New York (NY) Times, pg. CY6:
There are more than 12 Indian restaurants to choose from along the two-block stretch of Lexington Avenue between 27th and 29th Streets known by some as Little India, by others as Curry Hill. The competition is fierce. Curbs along the strip look like taxi stands, jammed by South Asian drivers who flock to the area for spicy kebabs and pungent curries.
1 February 1996, Village Voice (NY), Robert Sietsema column, pg. 15:
Traditionally, Manhattan's best inexpensive Indian restaurants have been concentrated in Murray Hill along lower Lex, in a neighborhood waggishly known as Curry Hill. The prices are similar to the cheaper joints on East 6th, but the Lexington Avenue places have the paradoxical advantage of serving from steam tables--meaning that the food is fast, and, more important, you can see it before you order. My favorite has always been East in the West (113 Lexington Avenue), where you get a doormat-size nan in addition to rice, raita, salad, and three steam-table selections for around $5.
17 January 1999, New York (NY) Times, pg. CY15:
Onward and Upward on Curry Hill
Neighborhood's New Prosperity Draws Some Wistfulness
8 August 2003, India in New York, Vol. VI, pg. 22:
The Curry Hill scene
Some of the better restaurants on Curry Hill (also known as Little India, on Lexington, between 26 and 31 Streets) that serve very good dishes under $10. Many of the restaurants also serve buffet.