Hi I am trying to move different set of curves that are on different layers, these curves are located in different points and so I want to orient the different sets in a grid, and once, the collection of curves are located in the first section of the grid, mirror some curves of the set, and then move(copy) each curve(of a specific layer) to a position in the x axis. So layer 1, will move x amount, layer 2 would move x amount. Finally I would like to bake each curve back into its own layer.

So far I have managed to develop the curves according to their layer outside of the grid, using the Lunchbox layer reference component, but if I orient the curves to the grid, I then cannot do the movement on the x axis. Would this be possible with GH or would I need a more complex script for that? Thanks!

Just think about it in terms of data organisation, not layers!
What you want to have is a data tree that has a main tree branch for each set, and each main branch has a total of three subbranches for each curve colour. This way you can always reconstruct which colour and which set your currently working with. After your done with your transformations and paneling, you can simply bake each curve to its corresponding layers, since your data organisation is solid. Grasshopper really doesn’t care about layers, but it it cares about data structuring. Layers are a tool to organise stuff in a human way on a stack.

Here’s an example of the data tree {i;j}, where i is the set and j the coloured curve:
{0;0}
green curve
{0;1}
yellow curve
{0;2}
blue curve
{1;0}
green curve
{1;1}
yellow curve
{1;2}
blue curve
{2;0}
green curve
{2;1}
yellow curve
{2;2}
blue curve

When you shift the tree paths, you get the curves per set:
{0}
green curve
yellow curve
blue curve
{1}
green curve
yellow curve
blue curve
{2}
green curve
yellow curve
blue curve

Grafting undoes the paths shifting.

Somehow, your file doesn’t really reflect what you show in the picture above. Maybe upload that file!