Interesting. Looking at them I think you can get the apparent contrast in LR in the same range as NX by crushing a few blacks. Slide the black point up a bit more in LR. Look at that black background sign witht he white script lettering. NX has no detail in that. All black. LR is preserving some shadow detail. Slide up the blacks and watch that disappear. After that I bet they will look very much the same in tone & contrast.
Now getting past my direct experience..... To simulate the Nikon Mode III stuff, I suppose you could fool around with the HSL sliders in Lightroom. Try increasing both Red and Green Luminance? That's where I would try to work it, anyway.
Try these camera calibration settings in Lightroom. They're not an exact match for Mode III, but they'll get you in the ballpark.
Red Hue: -25 Red Saturation: +35
Green Hue: 0 Green Satuation: +10
Blue Hue: +10 Blue Saturation: -25
Depending on which contrast setting you prefer in Capture or in-camera, you may need to adjust some of the other parameters as well. A "normal contrast" setting in NX is similar to a "strong" contrast curve and a contrast setting of around 30-35 in Lightroom. These settings work fine in ACR as well.
In practice, I have presets in Lightroom and ACR called Mode III Color, Mode II Color and Mode III Default. The first and second simply change the values on the camera calibration tab, with the Mode III one using the values I just mentioned, and the Mode II reflecting zeroed settings. Those enable me to quickly change between two different color palettes. The Mode III Default setting incorporates color mode, tone curve and contrast values and gives me the equivalent of Mode III and a normal contrast curve. It replicates a combination I use frequently with Capture.
Thanks. No, I don't. I've played around a little with it, but haven't replicated it so far. I have something that's close, but the real Ia in NX gives slightly rosier skin tones for subjects with light colored skin. I may post those settings later in case anyone wants to experiment with them and refine them.
Incidentally, the latest version of the Mode III preset I'm using (it's really III rather than IIIa although the differences aren't huge) has a slightly different red saturation value: 50 rather than the previous 35. This seems a little closer in my opinion, but if you like what the other is giving you, that's all that counts. There's nothing magic about exactly replicating the Nikon color modes; there's a very broad range of color palettes that can look good in photos.