Laverne Cox has a busy schedule. She’s shooting the CBS legal series “Doubt,” but just three weeks ago she was on the set of “Orange Is the New Black,” for which she’s returning as Sophia Burset in season five. And on Oct. 20 she’ll be seen in Fox’s reboot of “The Rocky Horror Picture Show,” taking on the role of Dr. Frank-N-Furter, a truly mad scientist. Oh, and in her spare time, she Snapchats with Adam Lambert.

What can we expect from this new “Rocky Horror”?
It’s a reimagining of the 1975 film. And when we say reimagining, it’s really a tribute to the first film and a tribute to the history and legacy of “Rocky Horror.” We’ve brilliantly incorporated audience participation into the film, which has been such an integral part of why it’s the longest-running film in history. It’s about celebrating the spirit of “Rocky” and honoring that. The first film is still playing in theaters, so we’re not trying to redo that, but pay homage to it.

Warwick Saint for Variety

What was it like stepping into a role made iconic by Tim Curry?
I had such a great time playing Dr. Frank-N-Furter; it was one of the most joyous work experiences of my life. I’m working on “Doubt,” a CBS legal drama, right now. There are so many moments where I have to do less — she’s a buttoned-up lawyer. With Frank-N-Furter, it’s no holds barred, and it’s rare you get to be on camera and be as big as Frank-N-Furter gets to be. That’s usually reserved for the theater. We had our rules for the world we created, but we got to play a lot, and it was so much fun!

Did you grow up with the original film?
I discovered it my freshman year at Indiana University before I transferred to Marymount Manhattan College. Some friends of mine were talking about it, and I had never seen it. We watched it in the dorm, and they were talking back to the screen, and I was like, “What are you doing?” It was so cool, and I was immediately transfixed by the film and the music. Frank-N-Furter just spoke to me. The gender fluidity of the character, the naughtiness and the sexiness. At the time I was existing in a gender-non-conforming space. I had a shaved head and wore makeup every day and hadn’t yet medically transitioned. And I was like, “Oh my God, this is me.” And now it is me! I’m the new Frank-N-Furter. I still can’t believe it.

Tim Curry is in the new version of the film, too. Did you cross paths with him?
Tim Curry plays the narrator in our film, and our first day of rehearsal here in L.A., Tim was there. He is delightful and funny and still very naughty and has that British sense of humor. He listened to me sing every single song he made iconic the first day. He was very sweet and complimentary.

You mentioned you’re at work on “Doubt.” What’s it like playing a more restrained character?
It’s really different. Cameron Wirth, the character I play, is a huge part of who I am. We’re defense attorneys, and Isaiah Roth, played by Elliott Gould, calls us freedom fighters. And a part of me is that. I’ve spoken out a lot in my personal life about issues important to me, so there is something very natural to me about playing Cameron. Cameron is probably more of who I am on a day-to-day basis than Frank-N-Furter is. But there is a campy and outrageous and uncensored side of me that I don’t always get to show publicly, and I do that with Frank-N-Furter. I’m highly aware that there aren’t a lot of trans people in mainstream media, and I try to walk a balance of being authentically who I am and trying to understand I’m representing a community. And that’s a responsibility that comes with this platform I have.

I had heard that Adam Lambert, who’s playing Eddie in “Rocky Horror,” was approached about auditioning for the Frank-N-Furter role at one point.
I read something about that. Adam and I were Snapchatting the other day …

You Snapchat with Adam Lambert?
Well, we met on the movie. And I was obsessed with him during “American Idol.” I called in and was voting! He tweeted me three years ago when “Orange” came out, and we’ve been Twitter buddies until we met on the “Rocky” set. I had read that they talked to him, but I was told initially that they had been trying to cast Frank-N-Furter and couldn’t find the right person who would not make people think about Tim Curry. After I screen-tested, they thought that would be me. To be honest, I don’t think you can ever forget Tim Curry as Frank-N-Furter, but I think I’m different enough, and what I bring is different enough, that it announces to the world this is something new and different.

There were reports that Adam felt Frank-N-Furter should be played by someone transgender.
I read that as well. I was in a conversation with my acting teacher today about casting trans people in trans roles. We understand in the entertainment industry that there are so many political and business decisions around who gets cast. Movies have to get funded; people have to have a name to bring in box office. My dear friend Jen Richards made this beautiful point about the general public, when they often think about trans people they might think about — as brilliant as Jeffrey Tambor is in “Transparent” — they might think about Jeffrey Tambor accepting his Emmy. And they think that underneath it all, a trans woman is really a man. And her [point] was that when straight men are attracted to us, they haven’t worked through their own internalized stuff and this societal misconception that trans women are really men. And when men specifically play trans women, it perpetuates that idea, and it perpetuates violence against us. And there’s something to that argument.

I also think there are so many creative reasons why people play parts. I’ve always been a proponent that as an artist, I would never want to tell an actor they couldn’t play a part. The reasons I trained for years to be an actor is so we can transform into other people and play other people. I know some brilliant actors who have played trans characters brilliantly. At the Emmys, I said there’s a lot of trans talent out there that never gets a shot and never gets in the room. We need opportunities to get in the room; there’s a lot of amazing talent and we should just have a chance. If Jenji Kohan and the folks at Netflix were not committed to hiring a trans person to play Sophia, I would not be here.

At the Emmys this year, Jeffrey Tambor said he would not be unhappy if he were the last cisgender man to play a female transgender on TV and urged people to give trans actors chances. How did you feel about that?

I loved it. I love Jeffrey. I love that he has embraced so much humanity but understands the political realities of what it means for a cis person to be playing a transgender part. And his is a really good example of how they needed an actor of a certain age who had not yet transitioned to play this part, and you maybe needed to cast someone cisgender. There are artistic concerns where we have to honor the intentions of the work. It’s a beautiful show, and what Jill [Soloway] has done insisting trans people work behind the scenes is wonderful.