How do I take settings (Brightness, Contrast, Saturation) from one image and impose it to another?

Original is the Background copy. Copy to be corrected is Layer 1

Highlight both layers and Edit > Auto Align Layers

On the Original use the Color Sampler tool to mark 3 aim points. Note on a scrap paper the values shown in the Info Panel.

Choose the Copy layer. The sampler positions are visible.

Image > Adjustments > Curves. Cmd+Shift with the Sampler tool on the 3 aim points. Their values now appear in the Info Panel and their positions on the separate curves are marked

Use the keyboard north/south arrow keys to move the curve point to the values marked on your scrap paper

These are the Curves that produced the Copy above. Additional aim points may provide greater accuracy.

You'll need to analyze the two images and then make necessary adjustments.  For example, read the tonal values in specific areas on both images.  This should help you understand brightness and contrast, and then from there adjustment layers can be utilized for the results.  Ask yourself questions such as brightness, contrast, and saturation.  You'll see that there are adjustment layers specific to these areas.

I confess, I'm not sure what you want either.  Maybe the Histogram panel will show you where the 2 images differ.   An old article but it's still relevant.

http://www.dummies.com/software/adobe/photoshop/how-to-use-the-histogram-panel-in-photoshop-cs6/

Bor sure what you mean exactly, please post screenshots of both images including all pertinent Panels (Layers, Channel, …).

If there are only two images why bother with a LUT?

If the changes you mentioned were made using Adjustment Layers then, with both I,mages open, click and drag an Adjustment Layer from one image over the other image. A copy of the Adjustment Layer will be added to that image. Drag each one in the same sequence as it appears in the original image.