Vaibhav Tiwari, 36, the son of former Domariyaganj MLA Prem Prakash Tiwari alias Gippy Tiwari, was called by some of his acquaintances from his home at Kasmanda House, Additional Director General of Police, Lucknow Zone, Abhay Prasad told the Press Trust of India.
Following an altercation, Mr Tiwari was shot dead, he said.
Gippy Tiwari was the BJP MLA from Domariyaganj in 1989, 1991 and 1993. In 2014, he joined the Samajwadi Party. In this year's Assembly elections, however, he campaigned for the BJP.
Vaibhav was the only son of the former MLA; a local BJP leader said that he reportedly had a love marriage with a non-Brahmin girl.
The police said that an investigation is going on.
The Uttar Pradesh Legislature is currently in session.