Stylized Procedural Toon Eyes with Procedural Eyelids

Stylized rig-ready cartoon eyelids controlled by very easy and simple material shaders (no fiddling with lattices and shape keys).  No need for shape keys or lattices.  You can scale the eye for different shapes as desired. 

File includes both stylized and simple toon eyes with procedural eyelids.

Lid Controls: The lids and eyeball rotation are controlled in the Materials Properties panel.  There are controls for top lid open/close, bottom lid open/close, and lid angles.  Since the eyes are procedural, it is best to view in 'material preview' mode in Viewport Shading.  The lids can be easily animated using drivers with whatever rig you choose.

Eyelid color is defined by the color ramp node in the eyelid shader.

Then change the colors on the color ramp. The middle color tab is the border color. Adjust thickness by moving it left or right.

A step by step video tutorial on how to rig the eyelids is here: Blender Tutorial - Rigging Procedural Eyes with Auto Rig Pro

NOTE: the tutorial is for geometry node eyelids, but it's the same process, just create drivers in the Material Properties tab rather than the Modifier Properties tab.