Police Lying Legality

For police to lie to a suspect - or anybody else - is not against the law and AFAIK does not violate "due process". Giving false testimony however - which two girlfriends were about to do - is a crime, called perjury. So the prosecutor actually prevented two crimes from being committed.

They also can lie when they interrogate you. They can tell you your friend has already implicated you in the crime, even if it's not true.

Yes, they can lie during an interrogation to make you confess. Not during a trial.

Doesn't perjury already apply?

Lying to the police, even by intentionally misinterpreting the question, is probably a bad idea.

Since it's trivial to show whether or not that is true, I would not advise making such a thing. It is highly inadvisable to lie to the police or courts.

It's illegal to lie to investigators. (They're allowed to lie to you, but not vice-versa.)

Cops can lie with impunity while in uniform, why would an undercover cop not lie to you?

This is actually their standard line, almost verbatim. Replace XYZ law with 'lying to me is illegal' and 'if you make this hard it will much worse for you and I won't be able to help you...' It is a long and well established right for the police to use deception to gain confessions. They will Mirandize you and then convince and cajole you into waiving your rights. They do it every day, and in almost every case.

They can't lie about them afterwards, but they can lie to you during interrogation. E.g. "your friend Joe already told us you did so you might as well admit it." even if that's not true.