As usual with AE there are few options:
the most complex and elegant I can think of is to split the line elements as well and have separate layers for the top and bottom outline. The fill, iris and eye front outline can be precomped and a mask can be animated to erase them as the lid closes ( the top and bottom outlines animate).
Then use Duik ( http://duduf.net/?page_id=151 )applied to Puppet tool pins (3 on each line) to animate the top and bottom lines to close and open.
Other option would be to just use Puppet Tool on the top and bottom outlines or distort them using Mesh Warp.