Do police lie during integation

This is a broad question. Have the police ever lied during interrogations? The answer is certainly yes. Do they always lie? Probably not. It really depends on the particular interrogation technique being used and the overall goal of the interrogators. The courts do allow the police to lie to suspects in certain circumstances as long as the lie is not meant to elicit a false confession (Hawkins v. Lynaugh (5th Cir. 1988) 844 F.2d 1132). As Justice Crooks of the Wisconsin Supreme Court once wrote: “using deception in an interrogation is common and generally accepted.”
One of the most well-known interrogation techniques involves separating accomplices and telling each that the other one confessed. Saying that the other suspect already incriminated them and that it will go better for everyone if they confess has often proved to be effective.
One interrogation strategy that police sometimes use involves lying about having physical evidence. Police might tell a suspect that they have their fingerprints or DNA linking a suspect to the crime, even when they do not. This technique was upheld by the 6th Federal District Court in the case of People v. Jones, when the court ruled that the practice does not violate the Constitution.
Another technique used in interrogations involves lying about there being witnesses. Trying to get a confession by telling the suspect that the police received an anonymous tip or that someone saw them at the crime scene is not uncommon.
There are likely many other ways in which police could lie during an interrogation. The important thing to remember is that, according to the courts, the use of deception does not violate the Constitution as long as it is not knowingly used to get the suspect to make a false confession.
https://inpublicsafety.com/2015/12/the-use-of-deception-during-police-interrogations-2/