You could do it in Fusion, using trackers and grid warp, but its definitely the purview of a VFX artist, and not something you'd want to do in any shot where you could avoid it, especially if the subject is speaking.
Basically what Jason wrote, although for lips spline based warps would be better. Roto the source shapes (original lips) and then animate target shapes as you wish to produce the warp.
Hendrik Proosa wrote:Basically what Jason wrote, although for lips spline based warps would be better. Roto the source shapes (original lips) and then animate target shapes as you wish to produce the warp.
Oh, I'm recoiling in horror as to how this could look...
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It would look like any other warp done in last 30 years. One good example of spline warping is the eyes of Mad Hatter in Alice in Wonderland which was also stereoscopic. Johnny Depp got his big eyes from spline warps, comps were done in Nuke.
Sorry for bumping into an old discussion. While I'm not sure about the specifics in Davinci Resolve, there are a few general ways to achieve this effect in video editing software. One way is to use the software's masking tools to isolate the lips and then use the scaling or distortion tools to increase their size. Another option is to use a plugin or effect designed explicitly for lip enlargement.