A lady who rocks -- Lady Gaga name -- talks to our Lee Cowan, for the record:

On a warm fall day in New York’s Central Park, Lady Gaga came to Strawberry Fields to pay her respects to John Lennon. “I used to come here probably four times a week to John’s memorial,” she told Cowan.

It was an unannounced visit, and yet it became an event. Everything around Lady Gaga becomes an event.

But by Gaga standards, it was all pretty tame.

Lady Gaga, with correspondent Lee Cowan, in New York’s Central Park. CBS News

“It seems like you’re more Lady now than Gaga, if that makes any sense,” Cowan said. “You know what I mean?”

“Really? Today,” she laughed. “What about tomorrow?”

There was a time when the one thing you could count on from the theatrical pop diva was outrageousness. After all, she put “meat dress” in the fashion dictionary. She wasn’t style over substance, though; her six Grammys are proof of that. It was just part of the package.

But her latest solo album -- her fifth, called “Joanne” -- is a toned-down diva.

She said, “I think that when people see me with less makeup on and less of what I was doing before …”

“There’s a sense you’ve evolved into something else?”

“Right. Oh, it’s less now. But you know, I don’t know that you can put a label on growth, you know? I’m just me. I’m just growing up. I’m 30, you know; this is what I want to do now.”

She debuted the songs in what she called her Dive Bar Tour. While there is plenty of dance pop for her “little monster” fans, the album is not, as she puts it, one big party. “There was a lot of crying,” she said. “Lot of crying, a lot of pain. A lot of learning about myself.”

The title track, “Joanne,” written with producer Mark Ronson, is about her father’s sister, Joanne Germanotta, who died of lupus at age 19, before Gaga was born. Gaga’s middle name is Joanne … and it’s also the name of her parents’ Italian restaurant on New York’s Upper West Side, where she and Cowan met.

“Playing the music for my father for the first time was very powerful, and my grandma, too,” Gaga said.

How did they react? “It was interesting: My father was very, very emotional. And my grandmother was too, but she held my hand and she said, ‘I hope, my dear, that you won’t be too maudlin while you’re putting this music into the world.’ What I think she meant by maudlin -- it’s an old word -- she didn’t want me to have an obsession with the death of my aunt.”

She calls “Joanne” her most honest record yet, including a song called “Million Reasons,” about the heartache of relationships.

Gaga’s own engagement to actor Taylor Kinney ended this year after five years together.

“I think women love very hard,” she said. “We love men. We just love with everything we have. And sometimes I don’t know that that love is met with the type of dignity that we wish it would be met with. You know, we’re not trying to make you less of a man. We just want you to love us as deeply and as wholesomely and as fully as we love you.”

It all makes for a pretty introspective sound -- one some critics thought might turn her fans off. Instead, “Joanne” has scored Gaga her fourth No 1 album.

“I think it is hard for them at times to, you know, change from album to album, ‘cause I go through quite a transformation. And that’s just the way I am as an artist. You know, they have to kind of let go of the last era of music.”

Cowan said, “When you were promoting your last album, you wore the world’s first flying dress ...”

“I have to laugh!”

“And this time, it’s dive bars is how you’re sort of releasing it.”

“You know, there’s just something fantastic and wonderful and humbling about being in a dive bar where I started making music and being able to sing this music.”

“Up close and personal to the fans, looking them in the eye for the first time when they hear it, it reminds me that if this were all to go away tomorrow, all the big success, that I would still be very happy going from bar to bar, playing music for people.”

“Would you really?’’

“Yes. The reason that I’m here at all is because of my relationship with my family and their encouragement of me to be a musician and to work hard. So as long as I stay there, in that space, I can do anything -- that’s my truth.”

Staying in that space wasn’t always easy. Her debut album, “The Fame,” was a huge hit, but Gaga had trouble washing off the persona she had created -- even for her own parents. “I used to come home and I think my mom used to watch me have a real hard time washing it off, you know?” she said. “I’d keep the wigs on and keep the make-up on, and kept the outfits on. I was always trying -- I never wanted to let my fans down, I always wanted them to see me in my art form.”

The only place Lady Gaga could be Stefani Germanotta was behind the closed doors of her own home.

“I’m very acutely aware that once I cross that property line, I’m not free anymore,” she told Cowan. “As soon as I go out into the world, I belong, in a way, to everyone else. It’s legal to follow me. It’s legal to stalk me at the beach. I can’t call the police or ask them to leave. And I took a long hard look at that property line and I said, ‘Well, you know, if I can’t be free out there, I can be free in here (indicating her heart).”

“And that’s what this album is? Getting to do whatever you want to do?”

“Yes, sir.”

“And not what people are expecting or imposing on you to do?”

Lady Gaga apologized for starting to cry.

“Is it emotional because you feel just that weight on you all the time, that fame is just -- ?”

“I miss, I miss people, sorry,” she said. “I miss people.”

“Just having normal conversations with people?”

“Yeah, I miss people. I miss, you know, going anywhere and meeting a random person and saying ‘Hi’ and having a conversation about life. I love people.”

Lady Gaga with corespondent Lee Cowan at Joanne Trattoria in New York City. CBS News

The one barrier fame didn’t put up was between her and her family -- especially her father, Joe.

“Making your dad happy is, especially for an Italian Catholic girl, I’ll tell you, it feels really good,” she said. “And I feel that today. You know, all the awards in the world, you can get into all the nightclubs, they’ll send you the nicest clothes. Nothing better than walking into your dad’s restaurant and seeing a smile on his face and knowing that your mom and dad and your sister are real proud of you. And that, you know, you haven’t lost touch with who you are. That, for me, is real success.”

In February she’ll take all she’s learned from these smaller stages to the biggest stage of all: The Super Bowl halftime show where, she says, it’s all in play: “Yeah, I always say, you gotta play a dive bar like you play an arena, and you play an arena like you play a dive bar.”

And, it turns out, she knows how to play Central Park, too. As she left, she saw a man with a bike, and hopped on. Only Lady Gaga would make an exit – side-saddle -- in a pink dress and heels, and somehow make it seem normal.

“You gotta love New York!” she laughed.



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