Ms Lankesh, 55, was the daughter of P Lankesh, a leading Kannada journalist who founded the Kannada weekly tabloid "Lankesh Patrike".
Her siblings -- Kavitha and Indrajit Lankesh -- are film and theatre personalities.
Ms Lankesh started her own Kannada tabloid "Gauri Lankesh Patrike" in 2005 after quitting as editor of the paper founded by her father, allegedly over differences with her brother who is also the paper's proprietor and publisher.
Ms Lankesh worked extensively for the rehabilitation of Naxals who wanted to to return to the mainstream.
(With inputs from PTI)