Nathaniel tells Jessica that Cliff, a member of La Résistance, is responsible for her father's death. In fact, Nathaniel struck down her father while fighting La Résistance; Cliff tried to save him. Nathan "reasons" that her father would still be alive, if Cliff had managed to rescue him — but since he failed, obviously that means he's responsible.
Cliff wasn't even on the same continent as her father, but Nathaniel reasons that, thanks to the butterfly effect, had Cliff acted differently, her father never would have died.
Nathaniel reasons that if Cliff was there, he might have been able to save Jessica's father.
Downplayed: Nathaniel tells Jessica the resistance killed her father. He was actually caught between a fight between the resistance and empire, and was not the only victim. Nathaniel reasons that had the resistance not engaged the empire in such a place, the people would have been spared.
Nathaniel tells Jessica her father would be alive today if not for the resistance, but some time after Jessica discovers that it's only true from a certain point of view, it is discovered that Nathaniel was told the La Résistance abandoned him to The Empireintentionally to save themselves. See also the example for Deconstruction, below.
Nathaniel does not like telling lies, but sees no problems in bending the "truth" around to make people come to their own conclusions.
Inverted: Nathaniel tells Jessica that he died fighting for the resistance. After she finds out he was a redshirt, she claims he lied to her, because he gave her the impression that her father was a major factor in the war.
Her father really was killed by the resistance. They lied to her to get her on their side.
Or: When Jessica confronts Nathaniel with the truth, he's just as surprised by it as she was.
Zig Zagged: It appears that the resistance fighter "Nate" killed Jessica's father, then approached her with this type of lie to get her on their side, but does it rather ineptly. When Jessica Spots The Thread and learns this, she abandons the resistance entirely. Cliff then finds evidence that Nate is The Mole Nathaniel and believes he killed her father and leaked the "truth" to her to avoid any chance of Jessica joining the resistance for real. On confronting Nate, it finally comes out that Jessica's father was The Mole and Nate was trying to protect her from that revelation - he was just bad at lying. Probably.
Nathaniel flat-out lies and has no logic, even shaky logic, to justify his claims.
He tells the truth, no matter how painful as it might be.
Nathaniel's cryptic comments on the subject could mean almost anything, and strings Jessica along by letting on that he knows something, but never telling her anything.
Lampshaded: Jessica responds to Nathaniel's lie by asking how accurate it really is, but otherwise accepts it at face value.
Invoked: Nathaniel intentionally allows Jessica to learn the truth after giving this type of lie in order to discredit his own side, while acting as The Mole.
Defied: Nathaniel points out that he could give this type of lie to make Jessica feel better about working with him, then tells her that she'll still work with him due to other reasons.
Discussed: Nathaniel considers how to convince Jessica to help him with a friend before approaching her, including the use of this lie and the possible ramifications if the truth emerges.
Conversed: "Well, that was a really vague and contrived way to be honest. Way to be, Nathaniel."
Deconstructed: Nathaniel twists the truth because he believes the Awful Truth would hurt Jessica too much, and he's afraid of losing her friendship. Naturally, when she finally learns the truth and turns on him, it's even more devestating.
Reconstructed: However, after some contemplation, Jessica realises that Nathaniel's intentions were in her best interests, and that if she had learnt the truth about her father's death earlier, she might have not been mature/discreet/strong enough to do the right thing. So she returns to La Résistance and proceeds to destroy The Empire and avenge her father.