If the police tells a lie, I would consider a "lie" only a factual lie. A lie about a fact. For example, if they tell you: a lady has witnessed you while you were killing your neighbour, and that is false, that is a lie. I would consider that a bad police work (also the law would consider it so).
If you find any claim about a factual lie said by the police in Knox's interrogation, on this case, then you can build the first part of your reasoning.
Which is the lie that the police allegedly told her?
The fact is, there wasn't any police lie. If you think the police told a lie, you should say what lie exactly you are thinking about, and bring some evidence about this.
But, let's make clear, that the lie that I expect to see in order to decide it is a police misconduct, must be a lie about a fact. Information that is factually false that is given purposely. Not a wrong opinion or a wrong judgement.
No. Even if there is a police misconduct, this does not shift responsability from the person wo declares. A misconduct by one, itself is something that does not justify any wrong action by another, it does not diminish anyone's moral responsibility. Even if the police is unethical, the suspect must behave ethically or, if he does not, the moral responsibility of his action will belong to him alone and not to others. This goes for each human being. Moral responsibility for one's choices is permanently personal, not depending on possible bad actions of others.