Gee, I always thought when people lie big time; they are covering up something.
You’re missing the point. In our criminal justice system people are innocent until proven guilty. The defense need not prove anything. It need merely throw doubt on the evidence presented by the prosecution. Here the evidence presented by the prosecution was scant- some circumstantial evidence but hardly enough by itself to support conviction and a group of impeached witnesses and one non-impeached (her brother) who was not wholly helpful to the jury. Did she lie? Yes. Did she probably kill her kid? Yes. Were her lies so she could probably cover it up? Yes. But did the prosecution successfully show beyond a reasonable doubt that she killed her daughter and then used her lies to cover up the fact she was the murderer instead of some ulterior purpose (e.g. to avoid criminal action even though she didn’t do anything)? No. The jury found not enough to support that.