Couple of things...

1) That isn't a true vertical lapse rate -- it's the temperature differential inside and outside of the eye, a measure of how strong the storm is. Generally, the greater the difference between the two, the more efficient the heating aloft within the eye is and thus the stronger the storm. Rita had a differential of something like 17C at its peak intensity; Wilma didn't quite get there. Maximum efficiency would be for the lower number to plummet while the eye temperature reaches that of the SSTs...generally we don't expect that and only expect about 30% efficiency from most storms.

2) Microwave data for eyewall replacement cycles -- best bet is the 85GHz products, I find...look for "moat" regions outside/away from the center with banding features forming into curved/circular shapes just outside of that. That tends to be a pretty good indicator of an eyewall cycle.

Would not be surprised to see some reintensification after this eyewall cycle is done...some theories are being floated out there about the trochoidal oscillations being a function of the inner eyewall rotating about the outer eyewall. They are with merit, but the exact cause is unclear. I prefer to think of the "storm spinning like a top" analogy -- spin a top and and let it move fast down a path and it'll wobble/spin some. Nevertheless, cool to watch.