When I speak to Lady Rizo, she is breastfeeding. We're connected over a patchy phone line from Edinburgh to New York on a mid-August afternoon, which is possibly the only time of year that Auld Reekie is noisier and louder than NYC. There's a car alarm going off on the Royal Mile, mere feet away from where I sit hunched over a landline, while street performers and promoters alike do their best to be heard over the strident ringing of the thing. Life on my end is clamorously hectic, but an ocean away, the cabaret star sits peacefully, her new baby at her breast, calmly musing about life, art, and the wonderful slog of the Fringe that awaits her. This sums her up perfectly: thoughtful, honest and unafraid to be exactly who she is.

The singer's new show, Multiplied, is all about her recent plunge into the world of motherhood, exploring son Tennyson's life from conception to birth. She's breastfeeding on the promotional material too, and when I ask if this is a supportive statement connected to the recent Free the Nipple movement, she explains that it's not really any kind of statement at all. It's just life, for goodness sake.

'It's reality,' she says, occasionally going quiet for moments as she tends to her son. 'If reality is political, then so be it. I think that more exposure of women doing and being what they are without apology is important in the world, and unfortunately we're still in a world where the quest for women to just "be" is still going on.'

While Lady Rizo seems to have no problem 'being', it's important to remember that she is actually 'being' a character, created by American comedian and chanteuse Amelia Zirin-Brown. The life, the love, the baby, they all belong to Amelia, but the show? That belongs to Rizo.

'I love the melding of reality and fantasy,' she says, explaining how she comes to construct her autobiographical performances. 'Where I find the reality is in the truth of my particular circumstances. Humour is crouching within truth, always. That's my own personal process.

'It's like I'm looking at my life through the lens of an alter ego. Lady Rizo is able to look at it all with humour and sensuality and glamour and palpable joy. She never has to deal with paying tax. She lives in the world that we all want to be living in, which is decadent, fun, social, spiritual and sexy. She grabs life by the cheeks.'

Lady Rizo and Amelia will both be doing their fair share of cheek grabbing this month, with Multiplied going centre stage at Assembly Checkpoint for the latter half of the Festival. The show is a mix of songs and stories, and when it comes to the bare-knuckle fight that is the Fringe, she's more than ready to battle her way through the crowds and critics.

'I guess it is like being in war', she says, reflecting on the frenzied nature of Edinburgh in August. She's using military vernacular, but in an ironic way: I asked her how she felt returning as a Fringe veteran, which amused her, since this will only be her fourth year.

'Are you a veteran after four years?' she asks, but I explain that the answer is yes. True, there are many acts that have appeared more regularly, but few who can match Lady Rizo's notoriety. In just three previous visits, she has established herself as the belle of the cabaret scene, impressing reviewers and audiences alike. 'I don't mean to compare myself to a war veteran, but I guess it is like being in a war. You feel embattled and brazen, and you have to keep really intense hours.'

Brazen is the right word to describe this performer. She is brimming with confidence, and has a power to connect with audiences. 'I am well versed in the art of mass seduction,' she admits. 'I like to make UK audiences especially nervous. They resist me at first, and then they give in.'

She draws them in with personal tales, original songs, and the occasional rearranged cover. Her mashup of the Pixies' 'Where is My Mind' and Judy Garland's 'Somewhere Over the Rainbow' is particularly memorable, for instance, but she's equally unafraid to tackle Beyoncé's 'Halo', or Nirvana's 'Lithium'. And the people? Well, they love it. Of course, it helps that Fringe audiences seem to enjoy performance as much as she does.

'I think it's like when you see people at sporting events, and it's so surreal for them to all be there for their team, and that sport. Well, shows are my sport. That's what I'm passionate about. To have so many people in a square mile that are diving into performance, it's just unlike any other place in the world that I've been.'

Her perspective on performance remains as passionate as ever, but her outlook on life has been impacted by the birth of her son. Now, she is more keen than ever to view the world with childlike purity, which informs her art in a positive way.

'I guess the brass tacks of my life as an artist has changed, in that I always have to think about this extra appendage, or this joyful little person that I have to be around. But as far as a larger, more expansive look at it, I think that as an artist what's really exciting is the gift of returning to infant eyes. It means just "being" in the way that babies just "be".

'You know, I'm very childish. I remember when I was eight years old and I was at an all-you-can-eat buffet. I ate so much and then I lay down in the booth and I had this thought: "I wonder if I'll ever be too old or too adult to not lay down in a booth after an all-you-can-eat buffet". I haven't gotten there yet. I am blatantly using the child to remind myself to always lay down in a booth.'

Maybe that's what audiences can take away from Lady Rizo's show: a reminder that life is art, art is life, and that no matter how old we get, there's always time to see a cabaret show, grab life by the cheeks, and every once in a while, let our inner child lie down in the booth.

Lady Rizo: Multiplied, Assembly Checkpoint, until 16–28 Aug (not 22), 6.55pm, £14-£15 (£12-£13).