Lai, 76, is the founder of the now-shuttered popular Chinese-language tabloid Apple Daily, which supported mass pro-democracy protests in the economic hub.
Detained in 2020, he is awaiting trial on charges including colluding with foreign forces and sedition.
In London, his legal team said they hoped Lammy would put Lai's case "front and centre" during his visit, which has not been confirmed by his department.
Lawyer Caoilfhionn Gallagher told reporters it had been "made crystal clear to the UK government" that if it is looking to reset relations with China, they "need to use that as leverage to ensure that Jimmy Lai is released".
At a Reporters Without Borders (RSF) event in London, Lai's son Sebastien said his father, who holds British citizenship, was in deteriorating health after being in prolonged solitary confinement for nearly four years.
"His health could get much worse at any moment," he added.
Lai's delayed trial began in December 2023 and he is due to testify for the first time on November 20.
"The (UK) government does need to stand behind him. Much stronger than they even have before," said Sebastien Lai.
- Lai 'a priority' -
Both the legal team and Sebastien have met UK foreign ministry officials, but Gallagher said they were disappointed neither Lammy nor Prime Minister Keir Starmer had yet met Lai's son.
"If this is a top-priority case for the UK government, why is Sebastien not being met by the foreign secretary directly?" asked Gallagher.
"Why is Sebastien not being met by the prime minister directly?"
Gallagher works for law firm Doughty Street Chambers, where Starmer made his name as a human rights lawyer before entering politics.
The UK Foreign Commonwealth and Development Office (FCDO) in response said Lammy had raised Lai's case when he met his Chinese counterpart in July.
"British national Jimmy Lai's case is a priority for the UK Government," an FCDO spokesperson added.
"We continue to call on the Hong Kong authorities to end their politically motivated prosecution and immediately release Jimmy Lai.
Lai denies the charges, which were brought under sweeping national security laws to quell dissent in the former British colony, which was returned to China in 1997.
If convicted, he could face life imprisonment. Six other senior Apple Daily staff are also in prison.
Britain has been critical of China's crackdown on press freedom and protests in Hong Kong, which has strained diplomatic ties.
RSF head of campaigns Rebecca Vincent said no one from the charity would be able to attend Lai's trial.
A staff member was detained and deported while trying to enter Hong Kong to monitor the trial previously.
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