Disclaimer: as usual my poor writing has led some people to believe that I am trying to say that you can’t use Lightroom or that Lightroom somehow opens RAW files the “wrong” way. Nothing could be further from the truth. RAW images are simply a dump of the RAW camera data when the photo is taken, and this data can be interpreted infinite ways to make a final image. Lightroom has it’s own way of doing it (by default) and that’s perfectly valid. The point of this post is simply to say “look, there are many ways a RAW file can be interpreted at the default settings by various software packages.” So, I’ve re-written parts of this post to better communicate this message.
Nikon holds the secret formula for what they believe to be the best way to decode their own RAW files. It doesn’t mean it’s the right way or the only way, but it’s the way Nikon has set up their camera and software to produce images. Adobe Camera RAW, the key to both Photoshop and Lightroom RAW editing, is not using this formula. I can’t speak much for Canon and the other camera makers (There are others? Kidding… don’t spam me) but I’m fairly sure it’s the same story everywhere. If you are not using the maker’s own software, you are not getting the same results. Usually people discover this by realizing that their RAW files don’t look the same as their JPG files. But the real reason is the RAW editor software, not any difference between JPG and RAW. A RAW file opened up in Nikon’s Capture NX will look the same as a JPEG shot in the camera. The same RAW file opened in Lightroom will look different. This is because that “secret sauce” formula for your Nikon camera is only programmed into Capture and not other apps.
That’s not to say you can’t create the same image using Lightroom or Photoshop. But it can be a pain.

Two Different RAW Applications, Two Different Results
Here we have crops of two typical scenes: a portrait and a landscape. Nikon’s version is on the left and Adobe’s is on the right. Both applications are set to default settings and a JPEG has been exported. As you can see there is quite a difference in color and brightness. I think most people would prefer Nikon’s version as it’s got more color values and skin tones are less blown out.
Does this mean you should use Capture and not Lightroom? Absolutely not. Lightroom RAW images can also be made into anything we want and Lightroom runs faster, works better and has much better options for sorting and organizing images.
Lightroom has many, many options that can be adjusted and saved. A collection of tweaks can be saved as a preset and then exported. I’ve created such a preset to help my Lightroom D300 RAW files look a bit more like Nikon’s settings. If you are curious you can download that preset here. (right click and save as) I haven’t tried the preset with other Nikon DSLRs but it can’t hurt to try.
This preset doesn’t match the Capture settings 100% or even close, but it does get closer (for me) to a good starting point. It’s mainly comprised of changes to color hue and luminosity, as well as minor camera calibration changes. It’s definitely an art and not a science, so I make no guarantees that it will work well for everyone. Here are the same photos with this preset, in Lightroom:

Skin Is Not Blown Out

Sky Color Restored (somewhat)
I’m not sure why Nikon, Canon and the others can’t give Adobe Camera Raw their custom settings. Perhaps they are trying to protect what they feel is their formula, or perhaps it is a technical impossibility. If anyone knows the real reasons, I’d love to hear. For now, there are many presets that emulate and create a certain look, and that will just have to be good enough. I would recommend that you take a series of images that represents what you usually shoot and come up with settings that work for you. Save those settings as presets or even Lightroom default settings. There is no need to stick to what Adobe, Nikon or anyone else thinks is best.