The burden of proof is going to be on LE to prove that the dogs weren't tired, and that the handlers didn't suggest a finding to them.
But perhaps lab tests of the carpet will be more definitive. If I were on a jury, though, I'd find it hard to accept even if Lisa's DNA. The floor next to the bed is a typical place for kid's diapers to be changed throughout their entire infancy - I've done it and so have all my friends.
I find LE's perpetual manipulation of the media - the dogs got a hit! - very disturbing. They have worked hard to try this mother in the media from day one. A confident police force, confident in their investigation and evidence, would not need to contaminate the jury pool by skewing public opinion so hard prior to presenting their case.