May I know which version of Lightroom are you using?
I am using Lightroom CC 2015.5.1
First thing to do in update to 2015.7.
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You only get the option to edit a copy when working with rendered files (jpg, tiff, psd).
When working with raw files, the file will open directly in Photoshop, and when you save it will be saved as a tiff, provided you have chosen tiff in LR's preferences under External editing.
What Per said above. When you send a RAW file to PS you never get that dialog window. When you send a TIFF, JPG or PSD file to PS that dialog box comes up.
The choice of whether the RAW file is saved in PS as a TIFF, PSD or JPG is set in the External Editing tab of the LR Preferences. Once set to one of those file format options in the External Editing tab of the LR Preferences when you click File > Save or Ctrl/Cmd + s the RAW file then gets saved to the format you chose.
it opens the NEF Raw file
This is the default way that Edit-in works for raw images. Nothing is wrong with this.
When both Photoshop ACR and Lightroom (embedded ACR ) are matching versions, Photoshop "understands" that Lightroom is the raw editor and the Adobe Camera Raw dialog (ACR) is not needed, so you do not see it open. ( "Matching versions... is the key to this answer)
You may see the filename tab in Photoshop show the raw filename (eg. 1234.NEF 1234.CR2 1234.DNG) but it changes to tiff or psd the very moment when you 'Save' the image. In fact if you close the image in Photoshop without making any edits then a new pixel image (tiff or psd) is not created at all.
If you want to 're-visit' ACR after opening the image in PS then you should instead use this to open the image- [Edit In > Open as Smart Object in Photoshop] then the layer thumbnail in Photoshop can be double-clicked to open Photoshop's ACR and re-adjust the image.
Victoria Bampton's flow diagram illustrates this for matching ACR-
Jim Wilde also explains in this thread-
Read in the second last paragraph starting- "In an environment where there IS compatibility of ACR....."