The 81-year-old Lee, who plays the wizard Saruman in the trilogy, said he had expected to appear in seven minutes' worth of climactic scenes.
The BBC said Lee now plans to boycott the film's premiere in December.
During a Wednesday interview on Britain's ITV1's This Morning program, Lee said: "As far as I'm concerned, I'm only telling you this because it has been revealed on the internet, someone has talked and it certainly wasn't me. I can't say any more because I signed a confidentiality agreement and I honor my word."
Asked if he would attend the premiere, he said: "No, what's the point? What's the point of going? None at all."
Lee, who also appears as Count Dooku in the Star Wars films, said appearing in the first two Lord of the Rings movie was "a dream come true".