#1, way too many poly's on this model, you could be well served using a 12-14 sided cylinder for this model.
#2, to get smooth deformations that your looking for you'd most likely be served tryign out the various deformers found under the animation menu subset
Swap to animation, on the file menu you'll see a section titled Deform, or deformers, i don't recall i just click it..LoL
within you'll find such as, warp, and lattice, twist, ect.
I think that the lattice woudl be a ood place for you to start to pull the lip out, and the warp would be nice to get the interior round shape of the lip.