I think "lying" by 3 year-olds is so ubiquitous that I consider it developmental. I think they confabulate and imagination and truth simply blur. I don't in any way reprimand my 3 year-old twins for lying or even try to really address it that much.
I'll give an example of how I handle lies. My daughter came into the living room holding scissors in her hand. She announced that she was NOT cutting hair. I noticed, however, several chunks of freshly cut hair on her shoulder. I just told her that it looked like she had chunks of hair on her shoulder and asked her to use the scissors in the living room.
In another example, I asked my daughter if she had eaten a bite of something that I knew had nuts in it. (She has food allergies). She said no, but I sensed she was scared of telling me. I just asked her again and told her that it was okay. I just needed to give her medicine if she had and asked her again. Then, she told me yes. I didn't even mention her previous "lie." They almost never lie about misbehavior.