Quote -
The trouble I'm having is that I have to open the lips to get the lips apart so I can try and morph them. But when I close the lips again, the morph looks weird for lack of a better word. The OTHER morph is interfering with the morph I'm trying to make. I'm not trying to make open mouth morphs is the thing ;o).

Well I know you're not trying to make open mouth morphs, and you just want access to the lips, which is why I uploaded that file above. In retrospect that won't work, because the lips are still closed and you can't get at the edges.
But you mentioned about needing a better open jaw or open mouth, so I assumed you meant you were working on some kind of open mouth/lip combo, which later seemed to not be the case after all.

As it is, there's no way you're going to be able to isolate the lips in Poser, to be able to get at them without opening the mouth. In Lightwave that's a breeze, because you can select just the lips, or make a selection set for anything and only what's selected will be acted upon. Then export the necessary part. Which is also why I mentioned that it would be good if Poser had a similar "select by material" feature, but also it would have to work in a way where your morph brush only affected that selection.

So I was just trying to figure out if I could make some kind of a hack file you could use to get at the lips, but I can't think of anything that would enable you to see what you need to, while only working on a specific area and not affecting all the surrounding geometry.