I'm using Slat. I made the animation with 15 fps. There are 91 frames total:
Frame 0: t-pose, no parts moved at all
Frame 1: keyframe (pose with "lungs full"

Frame 42: keyframe (pose with lungs almost empty)
Frame 50: keyframe (pose with lungs empty)
Frame 90: keyframe (practically the same as first keyframe, just not quite full lungs)
In-between frames are blended/tweened, of course.
I noticed there were some options checked under the anim menu, and I didn't know what they were for or if they were affecting this:
toggle 'Smooth frame transitions'
fix bvh 180 problem
toggle 'fix y rotation errors'