"Even at this late stage I hope they will see that in a modern world it is not appropriate to put a man with mental illness to death," Lewis said.
Lewis made the comments after a meeting with China's ambassador to Britain Fu Ying, which he described as a "full and frank exchange of views."
If the death penalty is carried out, Shaikh would become the first national from a European Union country to be executed in China in 50 years, according to the charity Reprieve, which is providing legal assistance.
Shaikh, a 53-year-old father-of-three, who supporters say suffers from bipolar disorder, was arrested in September 2007 in Urumqi in far western China with four kilograms (8.8 pounds) of heroin.
Sentenced to death last year, Shaikh lost his final appeal in China's Supreme Court this month. Campaigners say he was duped into carrying the drugs for a criminal gang.
Lewis said: "The clock is ticking and a man's life is at stake as we speak."
"We hope that the relationship that we have with China will count for something in the end. And that they, at this very, very last moment, will make the right decision and do the right thing."
He said the government has made 27 appeals to China over the last two years about the case, including by Prime Minister Gordon Brown to China's leaders.
Around 40 relatives and supporters of Shaikh, including his brother Akbar, held a candlelit vigil outside the Chinese embassy in London to call on the Chinese authorities to spare his life.
Seema Khan, a cousin of Shaikh, said the family "hope and pray that the Chinese government will reprieve him even at the last minute."
"I grew up with Akmal and I know that he would never knowingly have become involved in something of this nature. He is an upright citizen who has never been in trouble with the law before," said Khan, from Essex, eastern England.
Reprieve said Shaikh had been informed on Monday for the first time that he would be executed on Tuesday.
Reprieve said new witnesses had emerged following publicity about the case, and their accounts backed up the defence claim that he was mentally ill.
Shaikh was obsessed with recording a song that would help create world peace, the organisation said.
Two British men, Paul Newberry and Gareth Saunders, both quoted by Reprieve, said they had helped him record a song in Poland and it was clear that he was mentally disturbed.
Newberry, a British national who lives in Poland, said Shaikh was a "very, very ill" person.
He said in a statement issued by the organisation: "I was probably one of the last people who saw Akmal before he left Poland in August 2007.
"I met Akmal in spring 2007 when he started hanging around the tent city that protesting nurses had set up outside the Polish prime minister's offices in Warsaw. The protest attracted a range of 'colourful' characters and he was one of them.
"As I was British and was with a British friend, Akmal latched on to us. Immediately it was clear that he was mentally ill, although he was a very likeable person, friendly and very open.
"However, he was clearly suffering from delusions and it seemed to me he was a particularly severe case of manic depressive."
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