In Joyce Cary's rite of passage short story, "Growing Up," rather than lying, I think Jenny is simply being evasive. It might seem that the two words are synonymous; but I think of lying as an intentional desire to mislead—often for some kind of personal gain—while evasion makes me think of someone side-stepping an issue that is too uncomfortable or confusing to face.
Robert is baffled by Jenny's (and Kate's) behavior and his injury. Perhaps Jenny is a victim of teenage angst: one minute she is disinterested by everything around her, and the next minute she is chasing the dog without mercy, only to turn her attention toward her father. First she and her sister scream:
"Paleface—Paleface, Robbie. Kill him—scalp him. Torture him."
They tore at the man and suddenly he was frightened. It seemed to him that both the children, usually so gentle, so affectionate, had gone completely mad, vindictive.
Robert is unprepared for this change in his daughters. When the chair collapses and the dog nips Robert's head, the injury (perhaps even the sight of blood) calms the girls, and they see to cleaning and covering the wound. Robert, however, it not so quick to recover. This side of his children is completely foreign to him.
There is foreshadowing with regard to the gap developing between Robert and the girls when Quick's wife returns home with a friend to see the pandemonium that has occurred:
Mrs. Quick...arrived...with her friend Jane Martin...Both were much amused by the scene...Their air said plainly to Robert, "All you children—amusing yourselves while we run the world."
This shows that Robert already perceives a separation between women and men; and then Mrs. Quick has lumped Robert with the children, making him feel further isolated. It is this sense that makes Robert decide that after tea is over, he will go to the club—to seek out the company of other men.
Watching as tea is served, the girls carry themselves with "demure and reserved looks," though they pass over Robert as if he were a guest. He realizes that perhaps the girls don't feel the same way about him.
Heavens, but what did I expect? In a year or two more I shan't count at all.
As Robert leaves for the club, Jenny comes up behind him—saying that she wants to check on the bandage on her dad's head to see whether it's secure; but I think she, too, is surprised by the change in their relationship. I believe that she is trying to gauge where she stands with her father, finding herself in an uncertain place—that space between being a kid and becoming a young woman.
First she says:
No, I'll get on the wall. Put me up.
This sounds very much like a child's demand, "Pick me up."
When they look at each other, she has "an expression he did not recognize." When he thinks she will laugh, she frowns instead, thinking something over. Then...
She was also struck by something new and unexpected.
While Robert has been trying to figure out what has happened, Jenny is doing the same from her perspective. Some form of enlightenment has come to her; she is no longer "daddy's little girl," and she cannot share whatever her realization is with her father—a man.
Jenny has crossed a line where she is no longer comfortable with her father, though she may well not understand the changes herself. She is not trying to lie to her father, but to comprehend her own unusual behavior and what happened between them that day.