In case of mesh already bent, whose volume should be preserved, it can be too complicated to use [Lattice modifier](http://www.blender.org/manual/modifiers/deform/lattice.html?highlight=lattice). Lattice can be edited with using [Curve Modifier](http://www.blender.org/manual/modifiers/deform/curve.html?highlight=curve%20modifier), but the last one may not be applied to it. And the results in this case will be rather unpredictable and bad looking ([for example](https://i.sstatic.net/fJUGN.jpg)).

You could edit Lattice by yourself in *Edit mode*, but why ? A good reason not to do that is that you won't be able to use provided curve as a desired shape.

A workaround is to create rig for the mesh.<br/>
You add armature, extrude it (I began from right to left). Then you parent mesh to armature (with Automatic weights will suit your needs) and grab / rotate bones as you'd like:

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

I used curve as a reference according to which I edited the bones:

[![enter image description here][2]][2]

**[Download file here](https://blend-exchange.giantcowfilms.com/embedImage.png?bid=487)**.


  [1]: https://i.sstatic.net/dvPVf.jpg
  [2]: https://i.sstatic.net/jRudc.gif