Final Fantasy VII
Lucrecia was a first class biotechnologist who worked for ShinRa under the direction of Grimoire Valentine. Following Grimoire's demise, she then became the assistant of Professor Gast and Professor Hojo when they were investigating a specimen excavated from the Northern Crater who later became known as Jenova.
Throughout the course of the game, we learn more about Lucrecia through either herself of Vincent Valentine and we learn that she is in fact Sephiroth's Mother.
Ashamed By Her ActionsLucrecia's appearance in Final Fantasy VII comes if Vincent Valentine has been acquired. Using the submarine, it is possible to find a hidden cave and inside Lucrecia can be found. We learn that she attempted to take her own life after what has transpired, but the Jenova cells inside her body have prevented her from doing so.
During their romance, Hojo impregnated Lucrecia. With her apparent consent, Hojo then proceeded to inject Jenova cells directly into Lucrecia's womb to see what effect this would have on her baby. However, when Sephiroth was born she wasn't even able to hold him and she had horrible dreams about the events that would follow soon after. It was for this reason that she took herself away from society and hid in a cave.
Is Everything Ok?During one of her conversations with Vincent, Lucrecia asks if Sephiroth is dead as she can't bare to think about the terror he is causing. To ease her suffering, Vincent tells Lucrecia that Sephiroth is dead; despite the fact he is still alive and is currently summoning Meteor.
Dirge of Cerberus: Final Fantasy VII
Minor Character / Flashbacks
Lucrecia's appearances in Dirge of Cerberus come purely from Flashbacks seen by Vincent Valentine, or via Shelke through her Synaptic Net Dive ability. They mainly focus on her involvement with Vincent Valentine and her unorthodox science experiments.
Lucrecia was obsessed with a theory revolving around Chaos and Omega, two beings which she believed existed. However, other scientists - including Hojo - thought her theories were crazy and couldn't understand why she continued to research redundant areas with such persistance.
Valentines Day Isn't Always HappyLucrecia was assigned to work with Grimoire Valentine and the two had a very amicable working relationship, as Grimoire was one of the few scientists who respected Lucrecia's theories. However, on one unfortunate day, Grimoire's research went horribly wrong and there was an explosion.
Grimoire tried to shield Lucrecia from the blast and was killed as a result. Lucrecia held herself fully responsible for this and was filled with grief. This pain was amplified when Vincent Valentine - Grimoire's son - was assigned to protect her.
I'm So SorryDespite their obvious feelings for each other, Lucrecia distanced herself from Vincent to avoid any further pain. This unfortunately lead her into a romance with her new partner - Professor Hojo. The two eventually married and Hojo impregnated Lucrecia.
When Vincent found out about the plans to experiment on her unborn child, he was livid. Hojo deemed Vincent a threat and "dealt" with him. Realising that she had inadvertently caused this tragedy too, Lucrecia, following Hojo's experiments, tried to find a way to save Vincent's life.
Creating A MonsterUsing her research, Lucrecia realised that the only way to save Vincent's life was to merge him with Chaos. However, even though the experiment was a success; there was no way for Vincent to control Chaos, something which caused Lucrecia great distress.
In a last ditch effort to make things right, Lucrecia inserted the Protomateria inside Vincent, which would allow him to control the Chaos within him.