Lauren was a genetically-engineered Human born during the 24th century.
As a child, Lauren's parents took her to undergo an illegal procedure called accelerated critical neural pathway formation, which dramatically increased her intelligence beyond what Humans would call genius level. This left her, however, with an overly amorous personality. She was prone to believing that many different men, including some she had never met, were in love with her. Lauren's delusions did not extend, however, to Jack. This was ironic as Jack often appeared to be the only man who held any kind of attraction towards her.
Lauren was taken into psychiatric care and lived with others like herself. In 2374, after it was revealed that Doctor Julian Bashir had undergone the same procedure, Doctor Karen Loews – the psychiatrist in charge of Lauren's case – took Lauren, along with Patrick, Jack and Sarina Douglas to Deep Space 9. Dr. Loews believed that meeting someone like them who had managed to fit in to normal society would be helpful to them.
Along with the others, Lauren studied Gul Damar's speech calling for peace talks between the Dominion and the Federation. Together, just by watching the speech, they were able to determine the entire saga of Damar's rise to power without ever having heard any of it before. Bashir was very impressed, and encouraged their thirst for knowledge about the Dominion. They asked to watch the holographic recordings of the peace talks, and determined that the Dominion was stalling for time to solve their shortages of ketracel-white. Had the Federation signed the peace treaty, they would have almost certainly lost the war.
Grateful to them, Starfleet provided Jack and the others with classified reports and war plans. They quickly determined that the Dominion was certain to win the war and that the only way to prevent the loss of billions of lives was to surrender immediately. Unsurprisingly, Captain Benjamin Sisko rejected this immediately. Jack, Patrick and Lauren attempted to take Starfleet's classified information directly to the Dominion, knocking Bashir out and leaving him in Sarina's custody, so they could win the war more quickly, thus saving lives. Jack miscalculated, however, as Sarina released Bashir who then stopped him from meeting with Weyoun. Starfleet, however, remained willing to listen to any ideas they had on how to win the war. (DS9: "Statistical Probabilities")
In 2375, Jack and the others escaped the institute upon hearing Bashir was working on a procedure that would cure Sarina of her inability to properly communicate with others. With Patrick posing as a Starfleet admiral, and Lauren posing as a science division officer, they took her to Deep Space 9 where Bashir was able to perform the procedure successfully. During this second visit to Deep Space 9, Lauren became infatuated with Ensign Nog. (DS9: "Chrysalis")
"I told you why I brought you here, remember? To meet that doctor, Doctor Bashir?"
"You know, the handsome one."
- Karen Loews and Lauren (DS9: "Statistical Probabilities")
- Julian Bashir and Lauren, of Miles O'Brien (DS9: "Statistical Probabilities")
"Genetically engineered mutants. Can't you tell?"
- Jack and Lauren (DS9: "Chrysalis")
"Don't get your hopes up, Julian. It's over between the two of us. I have a new man in my life. That gorgeous little Ferengi."
"Jealous? That's so sweet."
- Lauren and Julian Bashir (DS9: "Chrysalis")
"Did you hear what she said? Did you hear that?"
"I don't think I've heard a more beautiful sound in my life."
- Sarina Douglas, Patrick and Lauren, of Sarina's successful treatment (DS9: "Chrysalis")
Lauren costume - It's a wrap
One of Turner's costumes was later sold for US$108.50 in the It's A Wrap! sale and auction
Lauren was played by actress Hilary Shepard Turner.
The script for "Statistical Probabilities" describes Lauren as "a beautiful woman of about [thirty-five], luxuriating on a nearby couch. Her name is LAUREN, and everything she does exudes a strange sensuality." This would put her year of birth around 2339. 
The characters of Jack, Patrick, Lauren and Sarina were collectively referred to as the "Jack-pack" by the Deep Space Nine writing team, with each character having a specific personality trait. Lauren was thought up by Ira Steven Behr as the sexy one in the group. According to David Weddle, "we all wanted to be in the casting sessions for her." (Star Trek: Deep Space Nine Companion, p. 513)
Hilary Shepherd Turner enjoyed playing Lauren. "Lauren was the most brilliant woman in the universe and a nymphomaniac. My husband say's she's the complete opposite of me!", she laughed. "She was described as being obsessed with Bashir, and very va-va-va-voom, but I decided to make her a little bit Hannibal Lector-ish as well." According to Turner, it was Director Anson Williams's idea not to let Lauren stand up. "The only time I ever stood was when I danced with Bashir" she recalled. However, this was planned by Williams to be a much more elaborate dancing sequence than appeared in the final episode. "Both [Alexander Siddig] and I are the biggest Klutzes" Turner admitted. "They had this whole overhead camera crane shot set up, but they had to kill it because we were stepping all over each other. Laura Behr is a fabulous choreographer and she was just saying, Ay, yi, yi! in exasperation. Finally they just had us keep our upper bodies looking like they knew what we were doing, but if you'd seen our feet, you'd have known we were just stumbling all over the place." (Star Trek: Deep Space Nine Companion, pp. 513-514)
When reprising her role in "Chrysalis", Turner found the singing scene difficult, despite the fact she had previously sung in an all-girl punk band during the 1980s. "I can read music and sing," she said, "but this was really hard. The song stuck in my head for months. I just thought it was very bizarre to be on Star Trek dancing in one episode and singing in the next." Despite this, she managed to get through the scene, even with fellow actor Tim Ransom shouting in her ear. "Tim! Oh, my god! He's tone deaf and he was singing right in my ear!" Turner recalled in amusement. (Star Trek: Deep Space Nine Companion, p. 615)
Two of the costumes worn by Turner as Lauren in "Statistical Probabilities" were later sold off in the It's A Wrap! sale and auction. The first, a dress with crinkled elastic and red tone print with a zip up back, was sold for US$127.50.  The second, a chiffon dress with patterned shades of purple, blue and green with long sleeves and a zip up the back, was sold for US$108.50. 
In his review of "Statistical Probabilities", Star Trek author Keith R.A. DeCandido described Turner's performance as "particularly strong." 
Lauren appears in the Star Trek: Typhon Pact novel Zero Sum Game along with Jack and Patrick. The three of them are working for Starfleet Intelligence in the year 2382 when they discover several startling revelations about the Breen.
Lauren at StarTrek.com, the official Star Trek website
Lauren at Memory Beta, the wiki for licensed Star Trek works