Folded surface with finger joints - Finding the L lines for the joint

Hi,

I am trying to create a folded plate surface with finger joints between the inner edges (marked green). 

I have my folded geometry in 2 layers (offset by t) as 2 meshes. I now need to find the 4 L lines, as shown by the figure on the right. 

Line L0 and L2 are easy, as the are a part of the mesh.

Line L1 and L3 however, I have no idea how to create for all my inner edges.

As you can see on the drawing they have to originate from the intersection points between the two meshes.

I've tried for days now, so any help will be greatly appreciated ! :)

/ Kirsten