Lina was born in a small village in Zephillia, the second daughter of merchants. Her parents owned what was in effect the town's general store, which helped build up Lina's love of food and money. Her elder sister, Luna Inverse, was the darling of both her parents and the town, excelling in martial studies and quickly beginning to make a name for herself.
At some point in her childhood, Lina concocted a plan which resulted in her deciding to seek a life abroad. Though it's unclear of her reasons (whether for profit or just childish mischief), Lina set up a magical device that projected an image over the entire town of her sister while she was in the bath. Luna's wrath was so great, that Lina quickly fled from the town and has been terrified of even the mention of her sister ever since. (In Slayers Try, Lina built an entire pyramid complete with tunnels and a sarcophagus to hide from a letter sent by Luna.)
This was likely Lina's push to attend a prestigious magic academy far away from home. Lina apparently did very well there, well enough to be assigned a color. In the world of Slayers, mages of great power or importance are awarded colors rather like titles, and most make a great deal of this, dressing in the color and introducing themselves with the full title. (Such as Rezo the Red Priest.) Lina, however, was completely embarrassed by the color she was awarded, and attempts to keep it a closely-guarded secret that her entire title is actually "Lina the Pink"
 Pre-Slayers TV series
Chronologically in Lina's life, the events of most of the movies, OVAs, and manga take place in the period after Lina's early life and before the Slayers TV series, in which she meets Gourry Gabriev.
At some point after leaving the magic academy and beginning her travels, Lina became acquainted with Naga the Serpent, an eccentric and extremely busty sorceress with an ego that matched, or even exceeded, Lina's own. Their friendship began after Naga continuously challenged Lina to a fight, and always lost.
While their relationship was adversarial to the point of straight antagonism, the two actually worked well together when they were on the same side. In their time together, they saved the world a number of times, and left an impression on a number of villages. Naga's presence, however, seems to have left less of an impression, despite being extremely tall, well-endowed, and scantily-clad. Many people are familiar with Lina and her skills, but no one ever inquires of her as to Naga's absence.
It was at around this period in her life, either just before or during her association with Naga, that Lina earned her reputation and nicknames such as "Bandit Killer" and "Dragon Spooker"; someone who tracks bandits and thieves and steals their ill-gotten gains for their own use. This makes her a somewhat questionable hero. On the one hand Lina rids the area of bandits, and on the other she keeps the stolen goods as her "rewards".
 Original Slayers TV series
At some point between the manga and movies and the TV series (and the original novels) in Slayers chronology, Lina and Naga have apparently parted ways. Lina proceeds to meet a man of equally questionable intelligence but formidable martial skills, Gourry Gabriev, when he "saves" her from a gang of bandits named the Dragon Fangs, Lina had injured the previous night.
Gourry soon reveals that he carries the Sword of Light (光の剣, Hikari no Ken?), a powerful magical artifact that Lina greatly covets. She announces her intent to follow Gourry around until he gives it to her and proceeds to do so. Around this period, Lina proves just how truly formidable she is by killing a fragment of the Demon Lord, Shabranigdo, with a spell called the Giga Slave, which she learned from multiple, unknown sources. Lina knew that the spell was dangerous, because when she initially tested the spell, she turned a beach into a "bay of death". However, Sylphiel tells Lina how dangerous the Giga Slave is and she refrains from using it until the next series.
Throughout her adventures involving Gourry, they are accompanied by a revolving band of adventurers including the chimera Zelgadis, Princess Amelia and the priestess Sylphiel.
During this time period she is 15 years old.
 Slayers Next
This story arc introduces Xellos and his machinations, along with further insight on the Mazoku. He appears first as a priest of a local temple offering information on the Claire Bible, a mystical artifact said to contain infinite knowledge. Lina is interested both as a sorceress and as a treasure hunter, while Zelgadis wants the Bible to see if it may contain a cure for his condition. All too soon, however, it becomes clear that Xellos is simply using all of them as pawns, although they don't discover to what end because he always ends most discussions with his catchphrase, "That is a secret!"
Eventually, the group gets caught up in a power struggle between two of the five Mazoku Lords, Chaos Dragon Gaav and Hellmaster Phibrizzo. Lina, temporarily deprived of her magic, eventually gains access to the Ragna Blade, one of two spells in her repertoire which draws upon power from the Lord of Nightmares. She also discovers that the true form of the Giga Slave is the Lord of Nightmares itself, and thus vows to never use it again, lest the spell go out of control and thus consume the world. Unfortunately for her, Phibrizzo is just as determined to have her cast it. In the final episodes of this arc, Lina does indeed use the Giga Slave at the cost of her own existence, becoming a host and vessel for the Lord of Nightmares. Lina is rescued and returned to herself, however, as Gourry dives into the Sea of Chaos after them, and the two of them share a passionate kiss (which they both appear to have forgotten after returning to their world.)
 Slayers Try
In this arc of Lina's story, she is recruited by the dragoness Filia Ul Copt to save the world. (Filia originally wanted Lina's sister Luna Inverse for the task, but Luna was busy with her waitressing job and foisted the task off onto Lina.) Reluctant to put herself in harm's way to save a world that is typically extremely ungrateful of her efforts, but nevertheless terrified of her sister, Lina sets off on the task.
During this time, Gourry loses the Sword of Light, meaning that theoretically, Lina now has no real reason to continue her association with him. However, she continues to do so in all facets of the Slayers universe, whether it be the manga, movies, or the novels and following anime season, Slayers REVOLUTION. In fact, in the latter two she mentions trying to help find him a new sword (and in the novels, eventually succeeds).
 Slayers Revolution
Lina gets arrested on false pretense which later comes leading her on a journey against another incarnation of the Demon Beast Zannafar. She also meets an odd little creature named Pokota, who also has the ability to use the Dragon Slave.
 Other Linas
Several different versions of Lina populate the Slayers world itself, due to various plots.
In one story in the manga, Lina and Naga are exposed to a mirror that creates an exact opposite of whoever looks in it. The user expects this to produce an evil and violent version of the two that would be only too happy to work for him and destroy the originals. However, what comes out of the mirror are a Lina and Naga that are sweet, kind, generous, and extremely concerned about the feelings of each other and everyone around them. Lina and Naga state that the mirror's true power must be to dissuade people "with sheer disgust". In their attempts to break the spell (and the mirror), the two actually wind up creating dozens of similar copies of themselves, which go on to found an entire village full of philanthropic Lina and Naga doppelgängers. A slightly adapted version of this story, which resulted in the mirror being destroyed without creating more than the initial doppelgängers, was used for one of the Slayers OVAs, commonly titled "Explosion Array" (after one translation of a spell in Lina's arsenal.)
Late in the first Slayers TV series, Gourry and Lina are both the subject of an attempt at cloning, which spawns a number of miniature, super deformed versions of them both. The super deformed clones fight to humorous effect, and after the mini Linas win, they all disintegrate.
Even more, in this case mostly lifelike clones of Lina were created by Xellos' master, Zellas Metallium in the Slayers RPG made for the Super Famicom console.
It is heavily implied to the point of outright statement that Lina and Gourry fall in love in Slayers Next, and in the original novel series. Other characters like Zelgadis and Amelia even take this for granted beforehand, and seem surprised by Lina's bad reaction when the notion is alluded to. There is a distinct lack of romantic development in the series, even after it is affirmed that Lina and Gourry love each other. In the Japanese publication Dragon magazine, The creator of the original novels addressed this by jokingly stating that he isn't adept in writing romantic scenes. The final climax of Slayers Next, the second season of the Slayers TV series, the two characters share a kiss, though they cannot later recall the incident. However, both Gourry and Lina remember that something important had happened between them. Gourry seems to fully intend to keep traveling with Lina anywhere she goes. In any media taking place after the two met, they have been featured together and should they ever get separated, are never apart for too long.