The singer and songwriter, who came late to her music career after years of cautious procrastination because of her father, likes to meet the people who like her music.
She knows some of them are Elvis fans but mostly these days, 11 years after releasing her debut record To Whom It May Concern, Presley is proud to call them her people.
The 46-year-old singer and songwriter loves that a lot of them are women her own age who can relate to the relationship dramas and existential crises she writes about. And then there is the 'large gay following' she adores for their support of 'strong women'.
'When people are looking at me, I don't know what they are thinking. Are they looking at my dad, are they seeing me for me now?' she says. 'By the time I am done with the show, I am my own thing. I am me and I don't do what he does.
'I am a singer-songwriter, just like Carole King or Joan Baez, which is more my vibe'.
The mother of four, including five-year-old twin girls Harper and Finley, returned to the studio a couple of years ago to make her third record, Storm and Grace, and return to the stage.
Reconnecting with the fans who had kept their faith in this bluesy rocker with the legendary surname has been her own saving grace.
'I love it, it's why I do it. After every show when I do meet and greets, I get to hear their stories. And their stories are heavy, you know', she says.
'They tell you about how a song helped them get through the big things in life - cancer, a death in the family, depression'.
'That's why I tour, that's what I want. I don't make money. I get out there to be with the people who listen and hear what they want to sayback to me'.
Presley certainly isn't doing it for the money. She doesn't need it. And for the first three decades of her life, she didn't do music at all because of the inevitable comparisons with her father. She didn't need that, either. But like a lot of the children of famed singers and songwriters, if the music is stamped on your DNA, you can only deny it for so long before it becomes a regret.
'I always wrote songs, even when I was a young child. I loved poetry especially and that was always an outlet of therapy', she says.
After a decade of regular shows, she is now comfortable on stage and not just looking at the faces to see who is there to see the daughter of Elvis and who is there to see Lisa-Marie.
'I can differentiate between them pretty quickly now', she says, laughing.
'I remember when I first got on stage I wondered what the hell I was going to do. And then I found out that the crowd's energy makes such a difference to how you perform.
'I had to develop confidence because I am not an innate lead singer.
'Lead singers are innately vain and that's something that I don't have at all. I am so insecure and really had to find way to stop being terrified and thinking I suck'.
Presley says her fourth husband, Michael Lockwood, is the 'boss', her musical director and father of the twins.
'He is the boss, he does everything and he has always done that for Fiona Apple, Susannah Hoffs and Carly Simon, who he has been a musical director for as well', she says. 'He knows what he is doing and he is an incredible musician', she says
Her daughter, Riley Keough, who is an actress with a role in the new Mad Max: Fury Road, will come to Australia for the shows next week. Her son Ben will accompany her for the Japan leg of the tour.
'The kids can't wait. My daughter has just started dating an Australian boy, she's in love with an Australian man. They met on the film', Presley says.
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