It is all die-off - which is a good thing. You are helping to kill the bacteria that causes Lymes which in turn is allowing your body to rest better. The cleansing is also causing toxins from the dead bacteria to leave your body through your blood. This toxic blood could be the trigger for the strange dreams.
After the anti-biotics, give it a few days, then go straight into the Lymes Cleanse. You body is responding well to the anti-biotics so I feel that it will also respond well to the Lymes Formula.