Lying

Dr. Terry Olson, Professor in the School of Family Life at BYU, writes, "Very few things frustrate parents more than having their children lie to them. This is partly because parents whose children lie often feel that they have "failed."" (17).

Many children lie at some point. Dr. Olson goes on to say, "Too often, parents condemn themselves unnecessarily," and then he gives great counsel for what parents can do who find themselves facing this problem.

"Often a parent's first impulse when he suspects a lie is to say, "I know you're lying! Now tell me the truth!" The trouble with accusing a child of lying is that you're practically inviting him to tell another lie. Why? Because if he's lying to protect his image of himself, and a parent puts on more pressure, he's going to protect himself even more "and the lie grows" (Olson 17).

Dr. Olson shares a story about a time his six-year-old daughter began to say she was completing her reading when she was not. 
These wise parents quickly realized that their daughter was hoping her parents would think well of her, and that "what was at stake was not just our child's honesty, but also something else very basic: our relationship with her and her understanding of where the lie might lead her. We first needed to make sure that she realized it was safe to tell us the truth, that we'd love her as she was, that lying just wasn't necessary" (18).

Looking for the Cause

Because lying often has an underlying emotional cause such as avoiding punishment or may be used to build up oneself when there are deep feelings of inadequacy, you can see that resorting to teaching the morality of lying may not be the best first step. 
Lying has a cause, find it and you often find the solution. For example, suppose you catch your child lying about who she was with and when. Why would she lie about this? Perhaps you would disapprove and punish her. If this is true, then why is she doing it? A child may perceive that acceptance, communication, positive relationships, etc. in the home are limited. This may lead our children to want to spend time with those who, they think, do offer these things--even in a way that may seem superficial and shallow to us.

An Increase of Love

"There is a handbook of human relations in the Doctrine and Covenants, section 121. In verse 43 the Lord says that when we rebuke someone when moved upon by the Holy Ghost, we must be sure afterwards to show forth an increase of love. 
"In the case of lying, it's sometimes a good idea to show forth the increase of love before, during, and after the rebuke. Children should always be secure in their parents' love. Lies come from fear and anxiety. Before the child feels safe in letting go of the lie, he has to sure he is loved and accepted and respected" (Olson 18).

Consequences

Lying is one way to attempt to avoid the effects of punishment. As you observe your child beginning to lie about his responsibility for certain actions, it may be a good time to assess whether avoiding unwanted or even inappropriate consequences may be the issue. 
Generally, the punishment should simply be requiring a child to make restitution: ""Caleb, you did hit Bryce in the face. No matter what you say, I saw you do it. Now how are you going to make it right?" The act has occurred; the child is guilty. The only question is, what is the child going to do about it?" (Cline and Fay 199).

Model honest behavior. Go out of your way to model the importance of honesty. Be alert to times when you are tempted to be dishonest, as in speaking disparagingly of someone in private but acting differently in their presence, or asking a child to tell someone on the phone that you are not home.

"The truth shall make you free," the Savior said (John 8:32). When parents help their children see that the truth frees them of anxiety, of unneeded guilt, or having to hide things from the people they love, such parents will be well along the road to teaching their children to "walk uprightly before the Lord" (D&C 68:28), (Olson 20).

Sources

Cline, Foster and Jim Fay. Parenting with Love and Logic. USA: Pinion Press, 2006. 
Olson, Terry. "When Your Children Lie to You," Ensign. Aug. 1977: 17.