Why do engine cowl lips appear larger and more blunt on the sides than on the top and bottom?
Images of 767 and 777 aircraft that I looked at show pretty uniform lips all the way around. This 757 engine (image below) looks thinner on the sides, which is the opposite of what you have seen.



The shape of the cowl (and lip) is going to depend mostly on the shape of the nacelle. The 757 engine (image above) has engine accessories at the bottom of the engine, which requires a thicker nacelle to cover, which requires a larger radius on the cowl lip to streamline. As discussed in this question, the 737 engines have a unique shape to provide ground clearance, so the accessories are pushed to the sides.