Asian Mediawatch, which has been urging members of the Academy of Motion Picture Arts and Sciences to vote against the film, says that the "Asian-American community is abuzz with concerns that the movie's critical acclaim legitimises a film that mocks the Japanese people".
Spokesman Tom Roman told Guardian Unlimited that the campaign may have influenced voting at the Screen Actors Guild (SAG) awards last week, where Lost in Translation star Bill Murray - hot favourite to win the best actor award - was defeated by Johnny Depp, who played Captain Jack Sparrow in Pirates of the Caribbean.
The outcome confounded many critics and industry insiders, but worse could be in store for the makers of Lost in Translation. Because the guild's members make up 22% of academy voters, the SAG awards are seen by many as a good indication of the way in which voting will go on Oscar night.
Mr Roman, who describes himself as "half Japanese-American", said that most of the people Asian Mediawatch had lobbied at screenings were either SAG or Academy voters.
"The majority of these people were willing to listen to what we have to say, and some of them even said that they would be returning DVDs they bought and asking for refunds. Reaction, overall was much better than we expected," he said.
"The SAG's voting block is obviously actors, and that has the majority in the Oscar voting block as well. And that's where we campaigned heavily. It didn't get best actor at the SAG awards, and hopefully it will go empty-handed on Oscar night.
"However, we are bracing ourselves for a best original screenplay win, since there is not much of a competition in that category, but we'll live with one Oscar. As long as it doesn't get best picture, director or actor."
Leslie Felperin, who writes on film for Sight and Sound, the Times and the Big Issue, said that she could understand if concerns over racist stereotyping swayed voters.
She said: "It is not a bad theory as to why Bill Murray lost to Johnny Depp at the SAG awards - although there were certainly other factors, too - for instance, many voters may have felt that comedy is often overlooked when it is actually harder to do than serious drama.
"People are quite politically correct in the US, and they get very sensitive if they are embarrassed about something.
"Last year was the first time that two black actors won Oscars, so the Academy's members will be feeling very good about themselves.
"They feel they have moved forward to a colour-blind casting - so any campaign suggesting that Lost in Translation is racist may give pause for thought, especially if the group has been effective at targeting voters' screenings." However, Adam Dawtry, the European editor of Variety, said that the racism issue would have no impact on Lost in Translation's Oscar chances.
"I wasn't even aware there was a campaign against the film. In my opinion, the film is not remotely xenophobic or racist. If it were really a clear-cut egregious case of racism, then it wouldn't have got where it did.
"I think that the case for racism in the film is very doubtful, and I don't think it will influence Academy voters at all."
Whatever happens at the Oscars, says Mr Roman, his group's campaign has given voters "an opportunity to open their eyes to the issues Asian-Americans and Asians face in American entertainment".
He added: "There has been some progress for the past few years, especially in American television, but this really should be an ongoing effort.
"Maybe next time when those people make movies or TV shows, they may remember this campaign and make more effort for better and balanced portrayals of Asian Americans and Asians. If that's the case, I think we are indeed successful. This is not a one-shot deal for us."
Focus Features, which produced Lost in Translation, did not respond to Guardian Unlimited's requests for a comment on this story. Neither did the Academy of Motion Picture Arts and Sciences.
What they said about the racism issue:
Director Sofia Coppola, interviewed in the Independent on January 2:
"I'm surprised [at the criticism] ...I can see why people might think that, but I know I'm not racist. I think if everything's based on truth, you can make fun, have a little laugh, but also be respectful of a culture. I just love Tokyo, and I'm not mean-spirited.
"Even on our daily call sheets, they would mix up the 'rs' and the 'ls' - all that was from experience, it's not made up. I guess someone has misunderstood my intentions. It bugs me, because I know I'm not racist. I think that everything you do, people could be offended by - unless you're just trying to be nice about everyone."
Producer Ross Katz, interviewed on CNN on January 29:
"We've shown the film in Japan, to a Japanese audience. The response was great."
Asian Mediwatch:
"The group feels that the film dehumanises the Japanese people by portraying them as a collection of shallow stereotypes who are treated with disregard and disdain.
"The film has no meaningful Japanese roles, nor is there any significant dialogue between the main characters and the Japanese. Such portrayals perpetuate negative stereotypes and attitudes that are harmful to Asian Americans in the US, where a significant minority of Americans already have negative attitudes towards Asians."
Kiku Day, the Guardian:
"Lost in Translation is being promoted as a romantic comedy, but there is only one type of humour in the film that I could see: anti-Japanese racism, which is its very spine."