Lykke Li wants to discuss many topics. The public persona of the Swedish singer-songwriter may be that of a guarded soul, the woman in black, a la Nick Cave or Tom Waits. But she does let the light shine through. It’s just that on her list of conversation subjects, “Lykke Li” is farther down.

“There’s a bunch of stuff I would like to talk about, generally, in life, that doesn’t involve me,” Li said last week. “I think it’s more interesting to talk about where the world is going: What can we do about the situation and politics in Sweden. Or what can we do about the drought in California. What we can do about Syria and the Palestinian conflict. (But) that’s a longer discussion.”

Li, who headlines the Fox Theater on Sunday in support of her third album, I Never Learn, wants to talk about how people should become more empathetic and build a stronger community. It shouldn’t come as a surprise from someone whose childhood was replete with move after move around exotic locales with her family.

The 28-year-old (full name: Li Lykke Timotej Svensson) moved frequently when she was young with her photographer mother and musician father: First around their home country, then to a mountaintop in Portugal, later Lisbon, Morocco, Nepal and India.

“I don’t have much to compare (my childhood) to,” Li said. “I was just trying to get by like everyone else. Sometimes I would be sad or upset that I could not be at home watching TV with my friends. Instead I was in Katmandu, sleeping on the floor without any electricity. I’m really thankful for it now because I realize it made me a world citizen.”

As a teen, Li tried dancing before deciding she wanted to sing. She worked menial jobs at grocery stores, bars, and waiting tables at restaurants. In her spare time, she sang at bars. One time her singing got her booed out.

“I was playing in an all-black hip hop club and I was trying to mimic Kate Bush, like, a really high falsetto,” the soprano said. “It was not the right crowd, or the time or anything.”

Yet Li pressed on, eventually moving to Brooklyn to record an album. Youth Novelswas released in 2008. It was followed by Wounded Rhymes in 2011.

“I was watching 8 Mile the other day, on TV. It really reminded me of that time (when Li was singing in bars),” said Li, who connected with Eminem’s quasi-biographical film. “I’ve been through that and I learned so much. No one can tell me that I haven’t fucking paid my dues to be where I am today.”

No one is more critical of Li’s music than she is. She has distanced herself from Youth Novels, despite its critically acclaimed reception (like all three of her albums). She compares listening to her early work to looking at a high school yearbook photo. Li values the lyrics and what she intended to accomplish, but slams her previous singing abilities.

“I couldn’t sing the way I felt at that time,” she said. “My voice wasn’t developed the way it is now. I was very young and inexperienced.”

Another thing she doesn’t want to be associated with is pop music. She wants no connection to musicians who don’t write their own music and lyrics. It became clear quickly that on this issue, Lykke Li has made a firm decision, and she’s not willing to back down.

“I see myself as more of a poet; a student of life. I was trying to tell my story in the most honest way.

“I kind of don’t even like getting labeled as a woman, because then people want to judge me for how I look, and all that. I really wish that it would be enough, what I’m trying to do with my art.”

Her art continues to be heart-baring, heartbreaking tales of love lost and deteriorated relationships. Leonard Cohen is a bit of inspiration and role model for writing gut-wrenching lyrics, but Li, ever critical of herself, says her poeticism does not compare to his, so she follows her own voice through the songwriting process.

I Never Learn includes stories about Li’s recent relationship, which disintegrated. The songs deal with a woman in her 20s, at a crossroad in her life, and dealing with pain. She notes that her “Saturn return,” which astrologers believe creates tension at the age of 29 (think of it as an early mid-life crisis), is approaching.

Li’s favorite song on the album, maybe the favorite of anything she has written, as of right now, is the title track, which paints a picture of a crime scene and describes love as a “place:” “Where the blue moon shines/ Where the tears melt ice/ In a sea of guilt/ By the fallen stars.”

Conjuring lyrics such as these, with a voice like hers, it’s no wonder U2 asked Li to sing on “The Troubles,” the somber, pained closer to their new album. Li recorded her parts about a year and a half ago, on invitation from producer Danger Mouse and Bono, and did a second take this summer.

Li enjoyed the challenge of singing back-up for the first time, she said roughly 60 minutes after the U2 album was surprisingly announced and released for free through iTunes; it was her first interview on the topic.

“That song (was) not fully in my key, and I realized that I’m not a real backing singer,” she said. “That’s actually a pretty hard job to do, backing up Bono….I realized, it was very fun to be out of my comfort zone.”

Before she began, Lykke Li made a goal to record three albums of music. She’s not planning to leave it at that, but she won’t push the issue, either. After this tour, she plans to take a break and let the next project or inspiration come to her.

“There’s not much to (the touring) life,” she said. “I dream of having a real life, of having a garden, having a family. Having Saturdays and Sundays off. That’s what I want to do next. I want to cook my food, and wash my clothes, and read some books.”

Follow Roman Gokhman at Twitter.com/RomiTheWriter.