*clears throat*
Vie de Marli was known for having several supporters to Sparda when he fought back the demons. Matier, Lucia's 'mother', is a descendant of one of them. Many years ago, demonic activity on Dumary Island, home of the Vie de Marli clan, began to heighten once more, and in the midst of the chaos, Matier found a girl... Lucia... who had demonic blood in her and was able to switch between a human and a devil form. Matier took Lucia in and trained her to become a warrior, to fight the demons that slowly began to take over their home.
The man who was behind the demon activity was Arius, a business man who was in search of more power. He had build some towering office buildings which were in fact making a gateway to the demonic realm. He started a project of making clones, using demon DNA together with human DNA, to create some supersoldiers. These supersoldiers are known as the Secretaries, beautiful women who acts as bodyguards for Arius. However, one of the clones were "broken" and was then thrown out as trash. That clone is Lucia who was later found and taken in by Matier.
However, the demon activity became more than Matier and Lucia could handle, so Matier summoned help from the son of her ancestors' ally - Dante, son of Sparda.
And that's where DMC2 starts.
You can read Tony's review about DMC2 here:
http://forums.devilmaycry.org/threads/devil-may-cry-2-plot.3682/