Lajmi was the daughter of painter Lalita Lajmi and niece of legendary filmmaker Guru Dutt.
Her brother, Dev Lajmi confirmed the news of her death.
"She passed away at Kokilaben Dhirubhai Ambani hospital at 4.30 am. She was suffering from chronic kidney disease and liver failure. She was on dialysis. She has been in and out of the hospital for three years," Dev told PTI.
He said the last rites of the director will be possibly conducted today.
Lajmi debuted as an assistant director under renowned film director Shyam Benegal, who was also her uncle. She went on to work as an assistant costume designer in Benegal's "Bhumika: The Role" (1977), starring Smita Patil, Amol Palekar and Naseeruddin Shah, among others.
"She was a niece of mine. She was a very fine filmmaker. She went through a long period of illness, it is tragic. She was much young to go," Benegal told PTI.
Lajmi made her directorial debut with the documentary, "D.G. Movie Pioneer" in 1978.
Known for making fiery films with women at the core of her stories, her filmography boasts of movies like "Ek Pal", "Rudaali", "Daman", "Darmiyaan" and "Chingaari"(2006), her last directorial.
"Rudaali" (1993) featuring Dimple Kapadia in the lead was India's official entry for Best Foreign Language film at the 66th Academy Awards. It also went on to win three National Film Awards, including Best Actress for Kapadia, Best Art Direction for Samir Chanda and Best Costume Design for Simple Kapadia.
Soni Razdan, a close friend of the director, said it is a heartbreaking news.
"She has been suffering for a long time. But she fought very hard. Unfortunately her body couldn't handle it. I did speak to her last Sunday and we were supposed to meet on Wednesday, but she was readmitted to the ICU," Razdan told PTI.
Earlier today, the actor tweeted, "Our dear beloved friend Kalpana Lajmi has gone to a better place. RIP my darling Kalpan. I shall miss you so terribly."
The director, who was going through a financial crisis, was supported by several celebrities from the film industry in her final days, including Razdan, Alia Bhatt, Aamir Khan, Salman Khan, Karan Johar and Neena Gupta.
Razdan said the director-writer had penned a book, "Bhupen Hazarika - As I Knew Him" on the veteran singer and her long-time companion, which she was planning to adapt on big screen.
"Chingaari", starring Sushimita Sen, was also based on Hazarika's novel "The Prostitute and the Postman".