The film is based on the real-life story of an impoverished 14-year-old girl kidnapped from her village in Andra Pradesh and forced into prostitution and who eventually testified in court against her traffickers.
Kukunoor, an acclaimed writer and director, will travel to London for the event, and will be part of a tete-a-tete following the film's screening June 1 at the capital's Tricycle Theatre.
Lakshmi stars newcomer Monali Thakur in the central role, with Ram Kapoor and veteran Satish Kaushik in key roles.
The film had its world premiere in January at the Palm Springs International Film Festival 2014, where it won the audience award for best narrative feature.
Among the other highlights of this year's LAFF are an appearance by filmmaker Vishal Bhardwaj; Pam Chopra, the wife of the late filmmaker Yash Chopra; and Indian-American comedian Nadia P Mansoor as well as films from Pakistan, India and Britain.