Lindsay Lohan on 'Relating' to Liz Taylor

While the world knows that Lindsay Lohan now has a new long-lost, half-sister, thanks to her father's airing his DNA test results on TV Thursday, she apparently was the last to know.

"I didn't even hear that, so thanks for the news," Lohan, 26, said on " Good Morning America" today when asked about the news that Michael Lohan has a 17-year-old daughter from a relationship he had with a woman while married to Lohan's mother, Dina.

Photos: Life and Times of Lindsay Lohan

"I don't pay attention to any of it. I can't," the "Liz & Dick" star said. "I don't really want to get into that because. I want to stay on the positive side of things."

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Staying positive is something Lohan has had a hard time doing lately, thanks to the tabloid buzz surrounding her estranged relationship with her father, a public dispute with her mom and questioning from authorities for things such as assault allegations that were later dropped, a hit-and-run and an alleged jewelry theft.

Now the star says she is refocusing her career, starting with her much-anticipated portrayal of Elizabeth Taylor in the new biopic, "Liz & Dick," premiering Nov. 25 on Lifetime.

READ MORE: First Look at Lindsay Lohan in 'Liz & Dick'

"I think that, and just as Elizabeth Taylor did, there was a time when I was just doing so much work constantly and I kind of had that moment where I was like, 'Do I really love doing this?'" she said. "And stepping back and seeing other people do other movies and then kind of noticing, 'Wait, that's what I love to do. I need to get in the right head space and just focus on being on set. That's what makes me happiest.'

"I'm reading scripts every day. I keep calling my agents. I'm like, 'Just keep me on set. It's safer that way,'" Lohan said.

Lohan, a former child star, put an equal force into nabbing the role of Taylor, a star with whom she says she shares similarities, from relying on her mother for support, to always being in the public eye to even spending time in the same rehab center, the famed Betty Ford Center in California.

"I had seen that they were going to be making the movie and I got the producer's number and started harassing Larry Thompson," Lohan said. "I didn't even care if my agents were doing it or not. I just did it myself, too, because I was like, 'You know what? I'm going to play this role, I have to do this."

"Elizabeth Taylor actually went to her mother a lot. She was really close to her mother, and I'm pretty much the same," she said.

Thompson, the movie's producer, told reporters in a conference call this week that working with Lohan was "not for the faint of heart" and that the production made him turn "50 shades of white," according to E! Online.

Still, the actress says she is happy with the finished product, and relieved that critics have not torn her performance to pieces.

"It's really nerve-wracking to play someone that's such an incredible force and a wonderful woman, so I was kind of nervous to see what people would think of it," she said.

Up next for Lohan is a movie, "The Canyons," that raised eyebrows when its trailer was released earlier this month as it appeared to play off the real lives of Lohan and co-star James Deen, who previously worked in porn. Lohan's character, Tara, is described as a "sensuous woman," and Deen, as a "potent new-screen personality."

The trailer also hinted that the movie might skip theaters and be "coming soon to an Internet server of your choice."

"I'm in a great place. I just want to move forward, keep working," Lohan said of her future. "I'm in the process of kind of moving and spending time with my family and just be happy."