Lattice modifier

Greetings,
I have problems applying lattice modifier to a specific vertex group. I am doing an origami, and figured out that if the lattice (u=20, v=2, w=1, simple deform and bend modifier with angle 200 and limit 0.67, 1.00) I use this to simulate folding the paper, but as whole, I cannot fold parts like step 4 in this diagram

my project is here, yet the json,html files are not updated.
link

Waiting for your advice.

Can you attach blend file directly here? It will take too much time to figure out where need to find needed file in your github folder.

Sure,
This is a working shape (didn't need to bother with this issue) Origami Heart

""You will probably find some pretty embarrassing dump stuff in the node editor, I was still learning and haven't cleaned them up yet ""


And here is project of the shape in the previous diagram (until step 3):
Aircraft

Ok, I tried to do it with lattice and it's seems for me that it imposible to do using this way. I think it's better to use bone system. I preper a little simplified example with bones, so you need to add some space between different pieces and do it more complex as you need.
origami.blend

I see,
Thanks a lot for the bone example, much appreciated, I will try it with bones this time. Yet I have been searching for a while how to use separated bones as one armature?! Because multiple armatures messes the fbx if I want to use the model in UNITY 3d for example?

I got it, just moving them will do! LOL
Lastly, this is about Blend4web, applying modifiers somehow stops playing the animation of the armature?! I wanted to apply solidify modifier but it will mess up the whole animation, so I have to make duplicate the plane I have and flip its direction to have a double sided rendered plane.

Here is the file after hell a lot of work
However, when I try the fast preview, it is significantly different!!!
Airplane2

I used "bake vertex animation" since I cannot use solidify modifier and animations, if it is possible, I would be most obliged to know how

However, when I try the fast preview, it is significantly different!!!

You need to apply scale before making an animation and baking it.