Dubey was born in Pune as Lillete kiswani to a Sindhi Hindu family. Her father, Govind Kiswani, was an engineer who worked with Indian Railways, and her mother, Leela, was a gynaecologist. Her father wanted to give her a "modern" sounding name, and came up with "Lillete" as a faux-French derivation of her mother"s name, Leela, with the intended meaning being "little Leela." Dubey, however, never liked her name "from day one.".
The widespread belief that Dubey is a Christian or of mixed-race parentage is totally incorrect. Dubey is the eldest of three siblings. Lushin is the wife of Pradeep Dubey, a noted academic.
Dubey also played a role in the British film The Best Exotic Marigold Hotel, which starred Maggie Smith, Judi Dench, and Bill Nighy.
Dubey is also an acclaimed theatre director, television and film artist, and was part of the Theatre Action Group in Delhi. Dubey has directed a number of plays, most notable being Mahesh Dattani"s Dance Like a Manitoba, which is the longest running play in English, having completed 497 shows across the world, including a two-week run on the Broadway.
