Eyelids may only be one or two lines, but they're also contribute to the general feel of the eyes. They can differ from person to person as well. You can draw the line very high above the eye (giving the latter a droopy, nonchalant air) or right on top (making the eye look more focused). Caucasians are often drawn with high eyelids since the droopy, nonchalant air can usually pass for the foreign look.
Eyebrows are important because everyone has them. I'm sure all artists have at some point in their drawing career forgotten to add the eyebrows, and sometimes it's not too noticeable. However, without the eyebrows, the face will always look like it's missing something. I mean look at the example below. Doesn't the first face just look creepy?
Eyebrows can be horribly bushy, or a thin curved line. They're more important than you think! Male characters usually have thicker eyebrows than female ones. If you accidentally draw your eyebrows too thick for your female character, she can end up looking like a guy even if she has long wavy hair, a dress and stilettos. Heck, with manga bishies these days, you just never know. So make sure you add your eyebrows in and adjust the thickness accordingly.
