Hi!
Thanks for the post.
The example file available here is a too much simplified version of the original including the street sweeper model (made by AndyD) . As it was not my own model, I didn’t post the complete file here.
In the original file, the lattice is parented to the street sweeper, and is not linked to the curve itself, so the lattice isn’t deformed in the curves, and the “water tape” is not deformed as well.
But all other problems are present. The “water tape” is deformed each time the lattice X axis points in its direction. It is also deformed in areas which are on transversal positions of the sweeper…
You are right, being able to adjust the area influence of a lattice would be very usefull!
Now, I have modified the curve used as guide, and everything is OK. The animation will be usable in a movie sequence, as far as we’ll show a short path without the curve coming back on its steps.
AndyD, I will put your street sweeper in situation in the part of the town that I have built for the chase sequence, and I’ll do some render test, as soon as I will have gone a bit further in my work. 
http://3d-synthesis.com/blender_miscellaneous/Lattice_Test_03.blend
Do not forget to open it in 2.40 a2!
Philippe.