A Supreme Court panel led by the Chief Justice of India has recommended Mr Lalit's name, along with three others, for the top court. The list will go to the Law Ministry, the PM and finally, President Pranab Mukherjee.
Mr Lalit represented Amit Shah - who was named BJP president this week - in cases involving the fake encounter killing of Sohrabuddin Sheikh and Tulsiram Prajapati in Gujarat. Mr Shah faces charges of murder and conspiracy in both cases.
The same cases were linked to the Modi government's rejection of former advocate general Gopal Subramanium, whose name was dropped from the list of four candidates recommended by the Supreme Court collegium.
Mr Subramanium had accused the government of launching a "dirt-digging exercise" against him for displaying "independence and integrity" when he assisted the court in the Sohrabuddin case. Sohrabuddin, a petty criminal, was shot dead by the Gujarat police in 2005, when Amit Shah was the state's home minister. The police falsely claimed he was a terrorist. Tulsiram Prajapati, a witness to the murder, was killed the next year.
Earlier this month, Chief Justice of India RM Lodha went public with his criticism of the government's move, saying Mr Subramanium's name was dropped "without his knowledge and consent".
The government cited a past Supreme Court ruling to say it had the right to seek reconsideration.
Mr Lalit will be the sixth lawyer directly elevated to the top court as a judge.
He has represented former army chief General VK Singh, now a BJP MP, Tamil Nadu Chief Minister Jayalalithaa and Congress leaders Amarinder Singh and SM Krishna.
He is also the special public prosecutor in the 2G spectrum scam case involving the gifting of out-of-turn mobile network licenses by the previous government to companies who allegedly paid big kickbacks.
The other judges recommended by the Collegium are Meghalaya High Court Chief Justice Prafull Chandra Pant, Gauhati High Court Chief Justice Abhay Manohar Sapre and Justice R. Banumathi, Chief Justice of Jharkhand High Court.