In trying to do this with a lattice modifier I find that the straight edges of my object become curved. I want to scale the object a certain amount at one end, not at all at the other end, and I want the scaling to be applied all along the length of the object in a linear fashion, i.e. in proportion to the distance from end to end. (The "ends" of the object are along the Y axis.)
I want to widen a guitar neck slightly at the end that attaches to the guitar body, while holding the width at the "nut" (where it joins the headstock) constant, and keeping the sides straight.