It is not a good idea to use Lightroom for comparisons, not even regarding "real world" results.
Lightroom uses various "under the hood" corrections and manipulations depending on the camera model. Important parameters like the black point, the default tone curve (which is not linear), the meaning of "zero" for sliders, etc. could depend on the camera model and/or camera profile chosen.
While Lightroom is popular and hence results could be regarded as what many users would experience, a test that only uses default (or equal settings) does not tell you what the potential of a sensor is, i.e., which noise levels would be visible if the optimal Lightroom profile and setting choices were made for that sensor.
I'd say that when it comes to sensor performance, DxOMark is a good source and if one really wants to do one's one test then a level playing field should be created by using a converter like dcraw that does not customise results based on the camera model.
Also, when it comes to "dynamic range", it does not make sense to distinguish between "highlight headroom" and "shadow detail". Dynamic range is expressed through a single number. Two sensors with the same dynamic range (at a given ISO value) may show differences regarding how highlights are rolled-off or shadow details are visible but these differences are then are caused by different post-processing parameters (typically different default tonal curves).
BTW,
DxOMark is generally in agreement with Michael's findings; below ISO 150, the D810 has higher dynamic range, but at higher ISO values, the A7RII is better.