The first thing to check when Library and Develop don't display the same colors is the monitor profile.
Try setting it to sRGB - here's how:
Press the Windows key + R, type colorcpl in the box, and hit Enter.
Add the sRGB profile, then set it as Default profile. See screenshot (from Windows 7) below.
If this fixes the problem, you should ideally calibrate the monitor with a hardware calibrator.
My monitor is calibrated with Spider. If I change my settings to sRGB profile, I still have the same problem. It looks to me as if the import "gives" the photo an other temperature. Instead of 5560K, the photo has a temperature of 5950 K. If I change the settings so that the photo looks good in Lightroom and I open the chaged good photo in Nikon View NX or just in simple Windows Photo software, the colors are wrong. The color problem only seems to exist in Lightroom.
These are classic symptoms of a corrupted or incorrect monitor profile. Try calibrating your monitor again.
If setting the monitor profile to sRGB didn't change anything, your monitor profile is OK, in which case Library and Develop should display identically. Are you sure they don't? Press E while in Library to enlarge the image, then press D to go to Develop.
Only other thing I can think of is the camera profile.
Try changing it from Adobe Standard to Camera standard.
I don't think anything is wrong.
When you first import the images into Lightroom you will see an image that was processed and saved in the RAW file using Nikon's RAW converter and the Picture Control profile you selected in the camera. Lightroom will update that image using the RAW converter in Lightroom and the default camera profile for lightroom, which is Adobe Standard unless you have changed it. Lightroom does not read your in camera settings for any parameters, so you will have to change them to get closer to the image from the camera. Adobe supplies camera matching profiles for the D810 with names of Camera Standard, Camera Neutral, Camera Portrait, Camera Landscape, Camera Vivid, Camera Flat, and Camera Monochrome. You can make any of these the default camera profile so it will automatically be used when you import a new image, but Lightroom will not automatically select based on what you selected in the camera.
The As Shot white balance value is a function of the RAW converter and it will never agree with what you see in the camera. Different RAW converters will give different values for the as shot white balance.
The color-temperature numbers depend on the camera profile, of which there are several, so if they are a bit off there's nothing to worry about. What's more important than the numbers is if neutrals are still neutral or not.
If your photos are showing dark then that's likely because you have Active D-Lighting or something similar turned on in your camera which purposely shoots dark then brightens the shadows digitally before creating the Nikon-rendering in the JPG or embedded preview.
Turn all those special modes off as LR is just starting with the raw sensor data and knows nothing of those other Nikon modes that apply ONLY to Nikon processing which happens in camera or in Nikon software, not Adobe software.