Parent Mouth_Top to the head bone, and Mouth_Bottom to the bone at the chin.

Parent the jaw to the head and we're done with our skeleton building.

Fig 5. Skeleton Hierarchy

Step3. Driving the Bones.

The joint chains are going to be controlled by clusters on a spline drawn along the lips.

Create a linear CV curve starting at the corner and ending at the middle by point snapping one vertex to each joint in the chain, giving you four curves in total.

Name them after the joints you just drew them over i.e. RTcurve for the right top curve, etc.

Figure 6. Lip Curve Clusters

Create a cluster for each CV in the curve. I prefer avoiding tedious tasks unless I'm billing by the hour, so I use the script clusterIt.mel by Malcolm Wright to create all of the clusters. (In case you're wondering, yes I do use a lot of scripts by other people, yes I am a lazy mook, and no I don't feel THAT bad for mooching, but thanks for asking).

Now that you have a full set of clusters, point constrain each joint to the cluster on top of it so when you're finished every lip joint is controlled by a cluster. It'll probably take you a few minutes, so I'll wait here 'til you're done. Finished? Good.