But there is still no sign of him this morning. Other than a few camera crews, the only one from the cast that is present is Taiwanese actor Chang Chen, last seen as Tony Leung Chiu-wai's love interest in Wong Kar-wai's Happy Together. The actor is looking rather lost among the chattering journalists.
The set is nothing more than a courtyard and exteriors and interiors of two old Chinese buildings. So far, location shooting has taken them through the southern Chinese region and the arid areas of Xinjiang.
It is 10am when a tired-looking Lee drags his way into the studio and is quickly hustled away for some private photographs with his producer. On his way, we hear snatches of his conversation: "It was better last night, I managed to get five hours' sleep."
Former Bond girl Michelle Yeoh hobbles in slightly later, balanced most elegantly on the arms of two crew members in a manner reminiscent of the Qing Dynasty empresses. The Malaysian-born actress is not pretending to be royalty - she is recovering from a serious knee injury.
Last to arrive is, ironically, the youngest of the stars, Zhang Zhi-yi. At only 20, the performing arts student has only appeared in one other movie, Zhang Yimou's The Road Home. But the woman said to be the mainland director's latest protege is as self-assured and poised as one who has been in the business for a long time.
Disappointingly enough, the other major superstar of the show, Chow Yun-fat, will not be showing his face. Bound by contractual agreements with 20th Century Fox, Chow is not allowed to be interviewed for any other movie until Anna And The King is released next month.
"If he could, he would be here doing the promotion rounds. He has higher hopes for this than he does for Anna And The King. He looks really good in this movie," one member of the crew divulges to me.
It is a sentiment that Lee shares, obviously, as he later describes Chow as a "drop dead gorgeous movie star". The 45-year-old film-maker does not think much of Chow's work in Hollywood so far but adds: "Those roles were worse than the ones he did in Hong Kong. But I think this film will add value to Chow Yun-fat. If it works, then he will be an international
In Crouching Tiger, Hidden Dragon - "don't forget the comma", reminds Lee, as it was left out in the promotional backdrop - Chow plays an upright warrior Li Mubai who joins woman warrior Yui Shaolian (Yeoh) in investigating the theft of Green Destiny, a sword filled with ancient powers. The trail leads to a bureaucrat's daughter Yu Qiulung (Zhang) and her lover, Luo Xiaohu (Chang).
The film is inspired by a five-part martial arts novel that Lee read many years ago. "I have actually put the first two parts of the novel together and mixed the stories of Yui and Yu," Lee explains.
"The title coveys two obvious meanings. On the surface is the daily life, the structured social codes and everything people do to follow them. Underneath all that is the hidden dragon, the repressed desires. It's all part of Eastern philosophy, all this calm exteriors. It's probably not
very successful except in the case of the Buddhas!"
By all accounts, this has turned into a most excruciating experience for Lee: he was telling journalists in London recently that he had lost nine kilograms while working on Crouching Tiger, Hidden Dragon. During the lunch break for the set visit, he promptly put on a face mask and went to sleep until awakened for his next interview.
"Everything about it has been tough," he sighs as he rests his head wearily on his hand. "If I had to pick one, I would say it was mixing a fine martial arts film - which to me is a B-movie in spirit - and pulp fiction literature and upgrading it to an A-movie with artistic values and
dramas in both production and cinema.
"In the production of a good blockbuster action movie that takes 100 days, they usually spend 80 days on action and 20 on drama. They just go blah blah blah and everything will take a hold.
"To us, the martial arts scenes are part of the progression of relationships and character building or plot. We have to choose many sites in different locations which is tough because the drama is also important."
If Lee had been looking for drama, he certainly found it about a week into shooting Yeoh's role. The Tomorrow Never Dies star did what she described as a routine flying kick and landed at "such a wrong angle" she tore the ligament in her left knee, two and a half months ago.
"Her injury affected the shooting schedule in a big way," admits Lee softly. "That's why this set was built. We were supposed to shoot in south China but we didn't have her so we only shot the exteriors while we waited for her to get better."
The wait took about eight weeks, during which time Yeoh had to have an operation on her knee and go through the painful process of physiotherapy and recuperation.
"It was a very easy sequence, not even a stunt. It's something I've done a thousand times before. It was an accident. Even looking back at the tape, there was no explanation," says Yeoh.
"When I was in America I talked to the doctor about the possibility of not going for an operation. I'd done it to my right knee before and it's a horrendous experience - not just the operation but the recovery process. It's slow and painful, but I had no choice.
"I called [producer] Bill Kong and Ang. At the time I was just a week into my role and I thought it would have been very easy for them to say, 'we have to continue' and change the leading lady. But I was told that never crossed their minds."
What the producers did, instead, was to rearrange the shooting schedule so that Yeoh's other big action scene could be done at the end of the shoot.
"It was a blessing in disguise that my dramatic side was heavier than my action scenes," adds the 37-year-old.
But that was one of the reasons why Yeoh says she considered appearing in "yet another martial arts film". She knew that Lee would be able to add something deeper to the action. "I think he has a dream he wants to pursue. We're very fortunate to be a part of it. He has a lot of things to say and he is able to say it in a very subtle and simple way."
Despite more than 15 years in the Hong Kong film industry, Crouching Tiger, Hidden Dragon is the first film in which Yeoh and Chow have worked together. The only other time they have worked together was for a series of commercials when she first arrived in Hong Kong.
"We've talked about it so often but never found the right project to work on. I guess we were just waiting for the right thing to come along - we've been waiting for the longest of times," Yeoh says.
And the experience has been even better than they expected. "It's like a camping trip. Even when it is not our scene, either Yun-fat or I would turn up on the set for a visit. It's almost like a family thing. We're here but it will be gone in a few weeks and we're never going to be in this environment like this again," she says. Most of the action scenes seem to have landed on the delicate shoulders of Zhang who, like Yeoh, is a dancer by training. To prepare for her role, she trained under martial arts director, Yuen Wo-ping, who wowed international audiences with his work in The Matrix earlier this year.
Still, it didn't help her overcome her discomfort at being strung up on the wires for days on end. "In the beginning I found it really tough because the harness presses on to your diaphragm and I often felt like throwing up," says Zhang, with a tiny pout.
At times like those, having old-timers such as Chow and Yeoh around helped a lot. "Sister Yang [Yeoh] gave me a lot of pointers on what not to do and how to tackle certain action scenes. She would also point out how certain actions differed and she would always remind me to put on protective padding," says Zhang.
But the one experience that stuck in her mind was the day she was particularly uncomfortable on a wire and she suddenly heard someone singing from a platform above her.
"It was Brother Fat [Chow] and he had seen that I was looking kind of pale. So he started singing to me. Then he called out, 'you're still young, you'll be OK. Look at me, I'm so old and I have been hanging like this for a few days!'."
It was one of the advantages of working away from Hollywood insurance companies and unions, says Lee.
"I hung Chow Yun-fat on a wire for two weeks - his feet never touched the ground - and I had no problems," he says with a smile.
The last thing Lee expected was to be doing a Hong Kong martial arts film, but that was what he found when he started work.
"I came back to China, where my parents are from, to make a Chinese film but I found that to do a martial arts film, you have to use a Hong Kong crew because they are the only ones who knew - from design to just production - what was going on. I was actually using the working model that Hong Kong film-makers had developed here in the past 10 to 15 years."
Despite the hardships, having the opportunity to give full flight to his fantasy and defy the laws of gravity has been "great fun" for the director.
"Sometimes when I was working with the crew I couldn't believe I was really doing it. I was like a kid, asking 'can I do it this way?'. When it comes to action film, it's pure cinema, very exciting and boyish. It's just a great adventure."