Confused about Lisa Spangler (Full of Spoilers)

I usually pick up on these things but it may have been too late when I was watching this. I don't understand the True motives of Lisa Spangler.

She seems to be working to suppress as she was following Caine to all the scientists, and was involved in the murder of Neely

When exposed by Caine it sounds like she was trying to say she was working for a semi-comunist organization that was interested in exposing the formula -- but this was another lie. Did I get this right?

But then she shot Tedesco who was responsible for killing Neely who had said those who killed Neely has been disposed of.

Why would she do this if she was on his side?