Lattice with relative influence

Hi all,

I am searching for relative influence of Lattice on a geometry. I can’t find the way how to do it in the version 2.8.

Just an example: fully rigged character with armature and you want to use Lattice as tweak deformer on one body part. In this case there is the most common usage of Lattice on the charater’s head for final secondaries as the irregular squash and stretch is(or any kind of global reshaping of the head, etc. …).
Is it possible to workarond the double transformation here?
When I am using Maya there is simple solution for this: the Lattice has the Base Transformation node so technically when you parent it under the Head bone the Lattice itself is capable of tweaking relatively to its “Base Shape” under the head bone and does not produce double transformations on the head components(vertices) even it is bound to joints/bones parented under head bone.

Thank you.