How to skew precisely a specific part of a mesh I'm trying to bend a object containing patterns at a specific locations. I need the bend to progressively skew the mesh and the patterns.
I've tried different things like using a curve or a lattice, but it's not precise and does not provide what I need.
I also tried directly editing the mesh, but still get the need to skew some part of it.
Here is the starting piece (it's hard to see but note that its height tapers from left to right and the pattern also get thinner):

Here is what I'm trying to get at (on the left bend, quickly mocked up in Photoshop after manually cutting and rotating parts of the mesh)

If I edit the mesh, I'm able to extend by extrusion the cut mesh to find out the place where the skewed point needs to be, so i know where to deform from/to, it's just there does not seem to be a tool to do it.

A lattice would seem the perfect tool, but since we can't exactly align the lattice with the mesh from object mode it doesn't work.
Some advice on how to get there would be much appreciated.
I think that a lattice would be a great tool.  As far as aligning it exactly, well, it's difficult (requires a bit of on-paper math) but it is possible.
However, an alternate, that's easier to set up, is to just use a mesh deform modifier:

In the bottom set of arches, the mesh deformer has been shapekeyed after the bind, creating (linearly interpolated) skew.  Note that the mesh deformer is displayed only in wire, so that you can see the interior mesh.
Note the top set of arches, which shows the setup but with the mesh deformer in the basis shapekey.  Notice that the loop cuts aren't placed evenly, as a lattice would, but are placed arbitrarily, wherever I want.  If you want to using snapping to align these edges with some edge of your base mesh, that's perfectly doable.