This is an important and difficult question. If we answer in the affirmative, then suspects are likely to know that they may be lied to by law enforcement agents. Still, they may nonetheless often be fooled or tripped up (they don't know when an officer is lying and when she is being truthful), and this in turn could lead to more convictions of guilty people which in turn would reduce recidivism and increase deterrence, thereby reducing the victimization of citizens by criminals.
I would think that a practice of telling lies that may be helpful for finding the truth (e.g., by eliciting a full confession) is justifiable if the reduction in crime it engenders is sufficiently large -- and this is quite large. Such a practice should be carefully circumscribed and supervised to minimize harm and to suppress abuse. And the lies should be revealed to those who end up not being charged -- and revealed also to those who will be charged, and before their trial.
Circumscription is important. Lies should not be very painful (e.g., telling a suspect falsely that his beloved mother has died) nor risk provoking a false confession (e.g., telling a suspect falsely that his buddy has implicated him and that he can save himself from the death penalty only by admitting to the crime in question). An example of a permissible lie would be telling a suspect falsely that a certain witness to what happened has survived and will be able to testify.