I think we should talk pot shape before lips, or perhaps at the same time, as it seems that different shapes, don't work with all lips.
Concave as opposed to flat sides, and angle or flair from bottom to top. It's easy on a purse shape, as that is super curvy. Seems to me that there are some angled straight sides on ovals and rounds that can go either way.
And then there are the lips. The most confusing part I think for me other than feet. (although I think I got the feet now.)
To me the curve that the lips add to the pot would seem like a feminine touch, but most of what I've read tells me the opposite.