Jagtar Singh Johal, a Sikh activist from Dumbarton, was in Punjab, northern India, for his wedding in 2017 when his family said he was arrested and put into an unmarked car.
He is said to have been tortured, including electrocuted, and faced the death penalty as a result of his campaign for Sikh rights.
In 2022, a UN panel admitted that Mr. Johal had been arbitrarily detained in India.
Mr Johal’s brother, Gurpreet Singh Johal, is fighting for his release and on Wednesday he met Mr Lammy.
Speaking after the meeting, he said: “Over the last seven years I have heard a lot of empty talk from previous foreign secretaries about my brother’s case.
“After today’s meeting I have much more hope that this new government will do what is right.
“David Lammy listened to what we had to say and the solutions we proposed – unlike his predecessors. But the proof is in the pudding – and that means getting Jagtar out of jail and back to Dumbarton.”
Mr Lammy is the fifth foreign secretary Gurpreet has met, following previous meetings with Jeremy Hunt, Liz Truss, James Cleverley and David Cameron.
He is also the seventh foreign minister since Jagtar was detained in 2017.
Dan Dolan, director of advocacy and policy at the advocacy group Reprieve, said: “The Foreign Secretary and the Prime Minister have taken strong, principled positions on Jagtar’s case in opposition, acknowledging that he is being arbitrarily detained and saying that the Government should demand his release.
“We urge them to honor these commitments. They have an opportunity to go one better than the last government and bring Jagtar home to his family in Dumbarton.
West Dunbartonshire Labor MP Douglas McAllister, whose constituency includes Dumbarton, said: “Jagtar Singh Johal belongs in West Dunbartonshire and bringing him home is very important to me.
“The Foreign Secretary has made it clear today that he is treating the case as a priority and I hope we will now see that in practice.
“His predecessors failed the family because they lacked the political will to resolve the Jagtar situation.
“I sensed today that the Foreign Secretary intends to do better and I hope, for Jagtar and the family’s sake, that we are already seeing that.”
A spokesman for the Foreign, Commonwealth and Development Department (FCDO) said: “The Foreign Secretary met today with Mr Johal’s brother, Member of Parliament and representative of Reprieve.
“The UK Government is committed to working towards faster progress on Jagtar’s case and FCDO consular staff continue to support Mr Johal and his family.”