The issue comes from the fact that of the use of a pole target that flips the plane of the IK chain bones by 180 degrees when switching between "left" and "right" side of the chain. The interpolation that is used for the Lattice is Catmull-Rom. For some reason the deformation of the Grease Pencil object is more pronounced using this type of interpolation even for small changes of the bones rotation.
The solutions are three - "too simple", "complicated" and "too much work, man"
If you want to compromise the lattice interpolation just switch to Linear Interpolation, add more W resolution and repaint your vertex groups:
This will practically remove the issue with the scaling but the deformation will not be so smooth.
The "complicated" solution uses drivers to "switch" the IK chain Bendy bones Roll In and Roll Out angles depending on which side of the IK chain the pole target is
It could get easily complicated if using vector math to get the position - so this is a simplified workaround that uses the IK bone angle as indicator where the pole target is. The IK bone is tracking the pole target using a Track To constraint.
If the Pole target is on the "left side" the Z rotation of the IK bone is negative and the Roll angles are set to 0 degrees.
If the Pole target is on the "right side" the Z rotation of the IK bone is positive and the Roll angles are set to 180 degrees.
Basically in both cases the Grease pencil Object is flipped due to the nature of the Inverse Kinematics Constraint used. So you can tell that this will work only with symmetrical objects like the one provided.
If you have an asymmetrical object the above solutions will fail.
In this case you should try to control the bending rotation of the IK chain not with a Pole Target but by enabling the Rotation option (under the Weight Position) in the IK Constraint Panel. On the figure below the pole target bone was removed from the rig:
In the third solution you have to animate both the location and rotation of the IK target bone, which some may find as too much work :)
Here are the blend files:
BendyBone02 - Linnear Lattice.blend
BendyBone02 - Drivers.blend
BendyBone02 -- IK Rotation Control.blend