I tried to get some sticky lips for one of my rig, and this is the kind of solution I came with (just a test for now, I don't know how easy it will be to set it up on a complex mesh but I think with some work it will be ok) The idea is to get the mouth opening by combining a shape key and a bone, both driven by their own joysticks which are constrained by a copylocation. A slider is driving the influence of this constraint and is so making lips sticky or not. Of course it is missing a lot more controllers (mouth height, rotation, lipsroll, etc...).

You can download this quick test video here (370KB):

https://drive.google.com/file/d/0B1IZmxfL5IEeZmRKODBScV8wN2c/edit?usp=sharing

The audio used for lipsync is from Gooseberry Trailer. So as the original licence is Creative Commons No-Derivatives Attribution 3.0, I hope it is ok as it is less than 5 seconds... The voice actor is Tom Hudson. If you want me to remove it, just send me a message.