I Need Help with certain color gradings

Looks to me like a fairly 'neutral' colour corrected image with the blues shifted toward the cyan and a bunch of saturation dropped into the blues/cyans (looking a the second and third link, the first has the blacks lifted kind of like what you see in VSCOcams filters).

But in terms of the 2nd and 3rd images, in LR, start with a neutral white balance and then under HSL you could shift the hue of the blues and aqua's to the left to give them more of that cyan tone. You may want to shift the yellows and oranges to the left as well to make them more orange-y red. This will complement the cyan tones nicely. And then in the saturation tab of HSL add saturation to the aqua's and blues. Your source image will need to have similar colour tones to start with otherwise you won't get the same effect (i.e. you need to apply a style to certain images, you can't just globally apply some colour effects to every picture and expect them to look good). But if you have a blue sky or blue water in your image that would probably be enough to start with.

You can do more with colour tones/ranges in photoshop using a 'Selective Color' adjustment layer. It will give you more control over these colour shifts not to mention being able to mask accurately if need be. You can see in the image with the hat where the cyan tone starts to come through the cream colours on the hat.

Looks like some nice dodgin/burning and retouching in photoshop too