Taking the new form, in which Calvin added a third opening, we began rebuilding the lattice structure. The above image shows the sequence of steps I took.
First I had to re-triangulate the edge of the new opening.
Then I traced each triangle with a polyline. In doing this could then go back and create surfaces from each planar curve. I then offset each triangle on their appropriate surface. Each triangel can now be extruded using the "fin" command.