Now, are you sure you're using the same profile in both programs?
In ACR, go to the Camera Profile tab:
And see what it says the profile is. Eg mine says this:
What does yours say?
Yes, of course. That's the point. When you have two screens, you get to choose the one that calibrates best, and make that your editing one; leaving the other for panels and email and stuff.
It doesn't have to be LED lighting, and it certainly doesn't need to be dimmable. The only challenge you face (and it's a big one) is positioning the prints in such a way that they don't get any glare from the lights.