Instead, she became a songwriter for hire, donating hits to the likes of Cher, Christina Aguilera and Rihanna (more on that later). Then fate came calling...
"I got an Instagram message from a guy in Greece who said, 'Hey, I really think your music would work over here and I'd like to license it.'"
"With all my experience, I didn't really know what licensing meant," says the New York native. "I figured it was for a film or television programme."
Instead, her mysterious Greek contact put out a single, Lost On You, and sent it into the Top 10.
Soon, the song was charting in Italy, then Sweden, France, Poland, Belarus and Israel. At one point, it was the fourth most Shazamed song in the world.
"It's just a wild thing to be going on," marvels the singer.
"I know all too well what it takes to have a hit: A little bit of luck, a little bit of work, a little bit of talent.
"I've worked with so many people, but I've never seen anything like this happen. I feel so lucky to be experiencing it."
In fact, the 36-year-old is so in-demand that she's speaking to the BBC as she boards a flight to Los Angeles; a task that's not without its pitfalls.
"Can you hold on for just a second?" she cackles. "I just found out I have to take six kilos out of my luggage because I bought so much crap over here."
Undeterred, she talks me through her story as she unpacks.
Pergolizzi's dad was a lawyer and her mum sang opera, but gave it up when she had a family.
Although it was a musical household (they listened to the classics, not the pop hits) her father advised against a career in entertainment, saying it would "never pay the bills".
But when her mum died in 1997, Pergolizzi finished high school, moved to Manhattan and pursued her passion; adopting the stage name LP after a nickname given to her by a camp counsellor.
"It's LP personally and professionally," she says, after I make the mistake of calling her Laura. "Even my girlfriend calls me LP."
Gigging around New York, she caught the attention of alt-rock band Cracker, who invited her to sing on their 1998 album, Gentleman's Blues. Singer David Lowery then produced her independently-released 2001 debut, Heart-Shaped Scar.
Enigmatic and androgynous, she cut a striking figure with her tumbling black curls and surgically-attached shades.
"I do rock the sunglasses," she concedes. "To a rude point, at times. But I don't care, it's my first defence. I'm shy, so I've gotta have something. I need some protection, man."
In 2006, she made a semi-legendary appearance at the music industry festival SXSW, triggering a record label bidding war.
Among her suitors was American Idol judge and all-round big cheese LA Reid, who signed her to Island Records - but their relationship quickly soured. (LP later accused Island of "taking a little tomboy and putting her in a dress").
To her horror, the pattern was repeated over and over again.
"I've had so many record deals now. I'm like on my seventh one. I've had so many chats about how much money I was going to make, it's shocking."
"Three or four record deals in, it feels like life has smacked you in the face."
Incredibly, she doesn't hold any grudges, taking a philosophical view of her "'quote-unquote 'failures'".
"Trying to launch a career as an artist is like trying to run through a crowd holding hands with five people. It's so difficult."
By 2007, she'd given up on the idea of solo success, becoming a professional songwriter after one of her Island rejects, Love Will Keep You Up All Night, ended up on a Backstreet Boys album.
Her big breakthrough came when she contributed to Rihanna's hit single Cheers (Drink To That), a dizzy, Jameson-swilling party anthem from the star's Loud album.
Incredibly, LP claims to have bashed out the song on a "cheap Hawaiian-brand ukulele" she'd brought along to the studio on a whim.
"It's a nice, off-the-cuff thing to bring to a session," she explains. "It's a little more organic. After we were done writing melodies, I could sit in the corner and write words with it, you know?"
She's since adopted the ukulele as her signature instrument - she even has her own, custom-made model from uke legends CF Martin & Company.
"Unknowingly, the ukulele started to worm its way into my heart," she says.
"I would sit in bed with it and whistle these little melodies. It was like, 'Wow, I love this. Maybe I should make it into a song?'"
"And that's where my trajectory of becoming an artist again came from. It was like me working my way back to enjoying music again."
But the main catalyst for her new material was a painful break-up with her girlfriend of five years. Lost On You is a primal howl, lamenting all the time she wasted on the relationship.
"Let's raise a glass or two / To all the things I've lost on you," sings LP.
"When I wrote that song, I was still about a year away from the breakup," she says. "It was like a long, winding, circle-the-drain situation."
The beginning of the end came when her partner asked to have an open relationship.
"The thing that upset me most was I knew she could see that I didn't want to go along with it.  But I tried it because I was really in love with her."
A couple of months into the experiment, though, LP fell for someone else. Hard.
"I was like, 'oops, I just fell in love with someone else'. And it's still going. I'm still with that woman a year and a half later."
"It's a happy ending - but also with some scars and some baggage, for sure."
LP's new girlfriend - musician Lauren Ruth Ward -  even appears at the end of the video for Lost On You, which the singer describes as a cautionary tale.
"That story is something you definitely don't want to hear if you're the person that decides to have an open relationship," she laughs.
It's easy to see why Lost On You has connected with so many people. LP sings with unfiltered angst about trying to wake up a lover who's lost interest; while the song's spaghetti-western arrangement betrays the hopelessness of the situation.
Like the lonesome cowboy she is, LP whistles throughout the track - sorrowfully echoing the hook and, at one point, apparently hailing a cab.
"I have a bunch of whistles I can do," she laughs, "and we were like, 'let's take my whistling to another level!'"
It's not very fashionable, though, is it? The last great whistling song was Peter, Bjorn and John's Young Folks 11 years ago, and it's not like people were gagging for a sequel.
"I feel good about whistling," protests LP. "A lot of people don't get it [but] I use it as an instrument.
"I do two things that are normally super-gimmicky, that I refuse to accept as gimmicks in my music: ukulele and whistling.
"I just use them unabashedly. Let's do both!"
Lost On You features on LP's Death Valley EP, which is out now on Vagrant Records.
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Signed and dropped by three major record labels, Laura Pergolizzi had all but given up on a pop career.