Why is there a Significant Color Shift between Develop and Library Modes?

I am placing a general response to this issue and then I will respond to each of you that helped.... Thanks! 

(btw.....I work nights, so I am at least 10 hours or so behind the last responses.) 

Since calibrating both monitors in early January of this year, I have had color issues.   I have two monitors.  One is an older but still fairly sturdy laptop that was originally loaded with Windows 7 and a Dell St24 monitor that was purchased about the same time.  Mid last year, I gutted the Laptop and a full version of Windows 10 was installed.  Color issues started almost immediately and in early January I purchased the i1Display Pro by X-Rite. 

The 1st issue was that the "old and loved" photo viewer that I elected to continue using after the Windows 10 install, would not recognize the newly calibrated monitors and the colors went absolutely crazy.   After abandoning that viewer and using Microsoft Photos to view exported images, the situation improved but it still was not great.   The final product out of Lightroom tends to have a heavier dose of "Green Tint" when viewed in Photos.  It is significantly noticed in an image with lots of light complexion skin tones visible.  It's not something that was significant in, lets say a group photo.     

In mid January, I took this complaint back to customer service at X-Rite.   Their explanation was that this is a Microsoft issue and not a Calibration issue or an issue with the unit I purchased.  I still have a problem with that explanation, because as a photographer, we want our clients to see the colors we produce, and if we are calibrating to a standard that most people with a typical store purchased Windows 10 computer do not have, then there is a bit of a problem, correct?  

Anyway, while on the phone with X-Rite customer service, we went through a totally new calibration of both monitors, step by step.  This is where I need to go back and evaluate the suggestions you good people have given me and see if something has 'slipped off  track' or see if there is a "difference of opinion" between your suggestions and the calibration instructions I got from X-Rite.    

Thanks!

PhotoJohnWS  wrote If I spend time editing a photo to reach a perfect color and then export it and It Turns Color on me.... What good is LIGHTRoom? Windows 10   Monitor is Color Calibrated with i1Display Pro Library Module on the LEFT and Develop Module on the right.

First, there IS a difference in how LR produces previews in Develop versus all other modules. The visual differences should be rather small and you MUST view both at 100% (1:1) to correctly preview the data.

Next, you state: If I spend time editing a photo to reach a perfect color and then export it and It Turns Color on me

If you see a difference between Develop at 100% (the most accurate way to be previewing the image) and another application outside LR after export, then that application isn’t color managed! Do check the display profile as suggested, do not let the software calibrating and producing an ICC profile to build what is called a V4 (Version 4) ICC Profile (check that applications settings/preferences).

Why are these screenshots from Windows "Photos" - which as we all know is not color managed at all?

But yes, a difference between Library and Develop is a defective display profile. No display profiles are "incompatible" as such, but if they don't follow icc spec, Lightroom will choke. So depending on which calibration software was used, LUT/table-based and/or Version 4 profiles tend to be problematic. Either because they're more complex to begin with, or because the specification isn't well established.

If they are correctly written, Lightroom has no problems with any particular profile types.