Well, everyone seems to be obsessed with the inhumanity of Lucy,'
Well, look at what happens in ep 8, <<they kill her dog, and shes bullied and picked on even before that>>, also look at poor poor nana, we see her chained up, bleeding all over. The director mentions that shes been used for "dangerous experiments". Obviously Lucy also underwent a lot of brutal torture in the name of science etc. Dont forget that shes Better than humans, being the next step in evolution and all. No way you would expect her to be merciful to any human, especially those in the research center. Prolly in the same situation as a Human <<with a lot of weapons>> trapped among Apes and other wild animals.
Getting back to the point, the dog getting killed is kind of "the last straw" for Little lucy, i mean even the bullies say "you dont laugh or cry", meaning she bore her suffering with silence. and also the dog triggers her "need to protect something" urge which is what releases her "arms/vectors". Kind of essential for the plot ^_^