Lid Controls: The lids are controlled in the Modifier Properties panel (wrench icon).  There are controls for top lid open/close, bottom lid open/close, and top lid angle.  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.

The eyeball rotation for the procedural eyes are controlled in the Material Properties tab:

Rigging Notes:

These are procedural eyes, so eye direction is determined by the material settings, NOT by rotating the eyeball mesh.  Since most rig controllers rotate the eyeball mesh, you will need to disable those drivers/constraints, and instead set up a driver on the eye rotation controls in the material tab shown below.

Similarly, for rigging eyelids add drivers to the geometry node controls in the Object Properties panel (shown below).  Disable any rig controls that move/shape the head mesh geometry for eyelids.

Parenting:

No need to 'join' the eyes to the head mesh.  Parent to a suitable bone that moves with head.  I find that 'relative' parenting often works best.  In the example model above, I used Auto Rig Pro and parented as 'relative' to the c_skull_02.x controller bone.