Nora's lies are engineered to protect the central deception she's created in borrowing money from Krogstad under false pretences. The irony of this is that it was done solely to obtain medical treatment for her husband. He's the principal one she needs to continue deceiving—and we can see why this is so when he goes into a rage at Nora upon learning of Krogstad's blackmail attempt.
All of this is symptomatic of the weak and dependent position of women in nineteenth-century society. Every effort Nora makes to continue hiding her past actions backfires upon her. She is forced to try persuading Torvald to promote Krogstad at the bank, although she knows Krogstad is the most untrustworthy person imaginable for this or any job.
When she suggests he is being "petty" in objecting to Krogstad's behavior, Torvald blows up, saying that "you must think I am petty." Yet even in this situation Nora's "lies" are ones of omission, not commission. The only real falsehood was the forging of her father's signature on the loan application. This doesn't indicate she's "untrustworthy" but rather that she was in desperation mode at the time, having no alternative except to let her husband die.
If it does say anything else about her personality, it might suggest that even in the context of the times, Nora is a passive-aggressive individual. Perhaps someone else could have found a different strategy than forgery, though under the circumstances it's not clear what this would have been. Ibsen deliberately withholds much of the detail concerning Torvald's illness that prompted the deception.
Without knowing all of the back-story we can't piece together the puzzle of this central event. But the main issue is that Nora, as a woman in the repressive society of the time, has been given few legitimate options to deal with a life-threatening problem.