The Hollywood actress tackles the part of the first female leader in the movie, but rumours emerged last year (11) suggesting Thatcher's grown-up children Carol and Mark were "appalled" by the film's plot.
And it seems Thatcher herself has no desire to see the film - she and her offspring rejected the chance to attend a screening of the project.
Lloyd says, "They were the first people we invited to see the finished film. They didn't take up our offer."
The director has previously attempted to reassure the family over the movie, stating, "I think that when they see Meryl's performance they will understand how much care and attention to Lady Thatcher's dignity she's given it. I think Margaret Thatcher was a superstar in this country and I think we all felt we needed a superstar to play her, somebody of huge intelligence, passion and power and warmth."