I am a child therapist who has studied human development in depth and worked with many children, in addition to having 2 of my own. So please believe me when I say...
4 year olds are not capable of "lying" as we adults think of it.
They are at a stage of cognitive development in which they use play and imagination to try to understand and figure out the world around them (their brain is unable to understand the difference between a truth and a lie). Because they do not understand the difference between make believe and reality (not in the same way adults do), once they make up a story (or what you refer to as a lie) they can come to believe that it is true. No amount of reasoning or punishment will help once this happens, as their little brains actually create a memory of the event! The image of a little boy with chocotale around his mother saying "NO mommy, I didn't eat a cookie" comes to mind. He will adamently deny to the point to crying despite evidence to the contrary, since now that he says it he believes it and remembers it this way.
The most important thing to look at and consider as a parent are the underlying needs that your daughter is exibiting through her stories. You as her mother are the expert here. The story about your son biting could be about sibling rivalry( wanting her brother to get in trouble), or maybe she wanted to know what you would do (after watching bad behavior in other children, maybe she wanted to know how you would react).
I would be very careful to not categoize these as "lies" and punish her, since from her point of view that is not at all what she is trying to do. I would teach her why her story was a problem and then I would begin looking at resources for addressing sibling rivalry (the book "Siblings Without Rivalry: How to Help Your Children Live Together So You Can Live Too" by Adele Faber and Elaine Mazlish).
But I would try not to give the story too much attention as that will reinforce the behavior. Children will live up to our view of them. If you think of her as a lier she will live up to this view. If you think of her as a child with a creative imagination, she will use this to become more adaptive in life. I am not saying not to try to teach them the difference between real and imagined, just realize that it will probably be about 3 to 4 years before her brain will be able to understand in a more adultlike way. Hope this is helpful.