When an officer places you under arrest, you should evoke your right to remain silent. Remember that anything you say is something prosecutors can use against you, and that includes any lies you tell.
Lying to a law enforcement officer is a crime of its own. If you do it, you can expect to face additional charges. But officers can lie to you in some instances.
A means to an end
Officers lie to try to get you to confess to a crime. They can tell you that they have evidence they do not or say they have witness statements when they do not. Officers can lie to you about the different aspects of their investigation as a means to pry a confession out of you.
But they cannot lie to you about your rights. An officer cannot tell you that you cannot request an attorney or that you must answer their questions, or you could face additional charges. The thing to always remember is you have a constitutional right not to talk, and if you say anything, the cops will turn it over to the prosecutor.
A problem for you
If you lie to officers, the story is a little different. You cannot tell them information that is not true. Since you did not use your right to remain silent, the prosecution can use your lies against you, and they probably will as proof you are dishonest. It can seriously hurt your case when you get to court because you will have proven yourself unreliable.
Your best option when under arrest is to stop speaking. You can provide your name and ask for an attorney, but beyond that, you should stay quiet. You can tell officers you are exercising your right to remain silent, but do not say anything else until your attorney says otherwise.