When designing electrostatic lenses respectively a specific field geometry, you have to consider general electrostatic properties. It's not clear to me, if you already did. One property is, that the line integral of field strength must be equal the potentential difference between the two electrodes for any possible path.
Furthermore, the field strength is a vectorial quantity, I can't see from your sketched function, what's the intended field geometry.
As another point, electrostatic lenses can be formed by electrodes only (plates, wires). So they considerably affect the field outside the target region. Arbitrary field geometries may be impossible in many cases.