There’s probably a few ways to do this but I’ll show how to deal directly with controllers, which is probably better information for future use of controllers.
Select the bone you want to control, go to the Motion Panel (1) then expand Assign Controller (2) select the Rotation Transform (3) and then click Assign Controller (4)
In the list of controllers that open up, choose the Rotation List and click OK. The rotation list allows you to stack some controllers. You’ll see the transform there changes and adds an Available option to the rotation transform.
So now you click on the Available slot and then add an Orientation Constraint. So this controller is what you ultimately need to do the weighting between bones. It can be added in a short cut way, but it’s good to know how these things work. So, the list is purely there to allow for stacking which you’ll see why that is a good way to set it up. You could actually just add the orientation constraint and that’ll work on it’s own but I’ll show why it’s good to stack it.
On the rotation list you can now see the Orientation Constraint in the list and when you double click on that you can now get the options for the orientation constraint. Now you can add the bones and when you’ve added the 2 bones you want to weight between (probably the 2 lip bones from top and bottom) you can pick them and type in weights for them. By default it would just be 50/50 weighting. You can actually put more than 2 if you wanted to as well.
You’ll see there’s an option to Keep Initial Offset. This is useful but only really works if you pick one bone to control with. This is mostly used when you set up a rig and you did not have your controlling object match your bone. but either way, this is why I use a list here because when you weight the bones, you’ll see now the bone orientation is based on the weights, so it’s no longer rotated like it used to be, and you can’t manually rotate it.
So now to get control back you can click on the Available slot and click Assign Controller and pick Euler XYZ. This will add the Euler controller into the list. Euler XYZ is the default rotation controller, it’s what allow you to grab and rotate something.
You’ll see the Euler controller in the list now and you can double click on it to make it active.
Now you can grab and rotate the bone again manually, so you can rotate it back to it’s original position. Because of the list, the bone will also be controlled by the weights you have set on the Orientation Controller. So you have the auto rotation from the weights plus the manual control on top of that.
You’ll see it’s also possible to weight the controllers in the list, so you can see how this can get fairly complex and powerful as a means to set up controllers for rigging.
So, there are other ways to do this, other short cuts to get things in there but it really is good to have a bit of understanding of how the controllers work. So, that’s why I wanted to show this method, though it’s a bit more time consuming. When you know how this works, then using the shortcut scripts will make more sense if you need to make modifications after the fact.