**Oblique projection Shear matrix to set lattice coords**

_Note: this is adjusting the lattice coordinates based on the shear required, not the camera. IIRC it has been asked as a feature request to add an Oblique projection to the camera, but AFAIK isn't available yet_

[![enter image description here][1]][1]

Without getting into too much theory believe this is pretty much shearing the coordinates of the lattice.

For a front ortho projection will shear the XZ plane (side walls) along the x, y vector (1, 1) or some multiple of it.

Test code, adds a cube with an encompassing default lattice and shears it based on settings for front view.

EDIT. Oops forgot to scale the lattice object not the data https://blender.stackexchange.com/questions/38335/how-do-you-freeze-or-reset-a-lattice

    import bpy
    from mathutils import Matrix, Vector
    from bpy import context

    shear_dist = 1 # sqrt(2) for (1, 1)
    shear_vec = Vector((-1, 1)).normalized()
    lattice_res = 8

    Sh = Matrix.Shear(
        'XZ',
        4,
        shear_dist * shear_vec,
        )

    T = Matrix.Translation((0, 0.5, 0))
    def mm(matrix, space=Matrix()):

        return space.inverted() @ matrix @ space
        
    bpy.ops.mesh.primitive_cube_add(
            location=(0, 0, 0),
            )
    cube = context.object
    bpy.ops.object.add(
            type='LATTICE',
            location=(0, 0, 0))
    latob = context.object

    latob.dimensions = cube.dimensions
    lat = latob.data
    lat.points_u = lattice_res
    lat.points_v = lattice_res
    lat.points_w = lattice_res

    latmod = cube.modifiers.new("Oblique", type='LATTICE')
    latmod.object = latob

    lat.transform(mm(Sh, T))

Ok have it better now, the leading face of the cube stays in place. 

Next step add shape keys for the projections eg TOP, LEFT, ... have FRONT

  [1]: https://i.sstatic.net/cbEe6.gif