It's entirely a product of Contrast through the use of Curves (or Levels).

Raise your black point in the curve (RGB curve).

Then lower the white point in the curve (RGB curve):

Then change to one of the individual channel curves and alter the black point slightly to put color into the shadow. For example your second image has a Yellow tint on the darkest portions.

Now alter the white point on an individual channel to put some color into the lightest portions. For example your second image has a blue tint on the lightest portions.

(You could split tone instead of the individual color channel adjustments, but its easier to just learn to adjust these curves)

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To verify I'm not making this up or guessing here's a basic analysis of your second example. Notice the histogram doesn't go from the left to the right but stops short of both ends.

The Lab of the Black Point (1) shows the Lightness stops at 16 instead of 0 (which would be black). The a is completely neutral at 0. The b goes positive which is towards Yellow.

On the Lab of the White Point (2) the Lightness stops at 87 instead of 100 (which would be white). The a again is neutral at 0. The b goes negative which is towards Blue.

So in this particular case they're flattening the the image (flattening the steepness of the curve) and then punching some opposing colors into the whites and blacks. The main thing for you though is the muted colors come from bringing down the contrast by raising the black point and lowering the white point.

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It's the exact same premise as the answer I gave here except this one is Landscape and in LR instead of a street photo in Photoshop: https://photo.stackexchange.com/a/88464/27243