Interpreting the phrase "lip faces down" in technical documentation
The edge of a hollow container or an opening.
Common example: A cup has a lip and it is often also referred to as a rim. In your case, it is the protruding side that moves away from the mesh; so, yes, the mesh side would go up and the side with a void would go down.
I THINK it means that the lip (as seen in the second picture)is at the bottom and the clear view of the mesh (third picture) should be at the top.
I say this as the membrane filter will need the support of the mesh as seen in the third picture.