He breathed his last at his home at Armanitola in Dhaka on Friday evening, his daughter Mum Minti Akhand Noor told bdnews24.com.
"He had high fever since last night. He could speak in the morning. I thought the temperature would go down, but it didn't," Mum Minti said.
The singer-composer was brought home on Apr 7 from Bangabandhu Sheikh Mujib Medical University after treatment there for two and a half months.
Ershadul Haque Tinku, who was close to the artiste, told bdnews24.com earlier that he had returned home on doctors' advice after his condition improved.
Tinku said Akhand was giving time to music after leaving hospital.
Cancer was detected in Akhand's lung in 2015.
He was later treated in a Thailand hospital after financial help was made available from the prime minister's fund. He subsequently underwent chemotherapy in Dhaka.
Musicians and music-lovers in Bangladesh have plunged into deep gloom at news of Lucky Akhand’s death. Social media have been flooded with pictures of Akhand, accompanied by messages of condolence.
Condoling his passing, singer Kumar Bishwajit told bdnews24.com: "I still remember when he gave me a song for my first album in 1977. I got a new life when he gave me another song, 'Jekhane Shimanto Tomar''."
"We will never forget his role in Bangla music. He will always be in our hearts," he added.
Akhand was a rage in the 1980s, when he hit the limelight as a singer, lyricist, composer and music director all at the same time.
His first album 'Lucky Akhand' was released by the record label Sargam in 1984.
"Eiye Neel Monihar", "Amay Deko Na", "Ritiniti Jani Na", "Age Jodi Jantam" and "Sumona" are some songs from this album that earned him a huge fan following.
After his brother Happy Akhand, one of the pioneers of pop music in Bangladesh, died in 1987, Lucky Akhand withdrew himself from music.
Then, after a decade, he hit the stage again in 1998, with two albums "Porichoy Kobe Hobe" and "Bitrishna Jibone Amar".
He had been a regular in many live music sessions on television ever since.
Born on June 18, 1956, Akhand worked with the record label His Master's Voice in his teens. He never looked back after that.
Information Minister Hasanul Haq Inu recently told a programme: "Lucky Akhand is the prince of music." The record label G-series honoured him with a lifetime achievement award at the event.
Akhand also composed popular songs sung by others, such as Kumar Bishwajit's "Jekhane Simanto Tomar", Ayub Bachchu's "Ki Kore Bolle Tumi", and Hasan's "Hridoyer Durdine Jachchhe Khora".
He had composed and directed music of Faruq Mahfuz Anam James' 'Likhte Parina Kono Gaan".
Other popular songs composed and directed by Akhand include "Kobita Porar Prohor Eshechhe", "Abar Elo Je Sondhya", "Ke Banshi Bajai Re", “Swadhinata Tomake Niye", "Neel Neel Saree Pore", Pahari Jhorna", and "Hothat Kore Bangladesh".