So in Lightroom go into Edit / Preferences / External Editing. You're given the output options for when you de-mosaic the RAW file into a rendered image format, tiff, jpeg, etc. Here you're given options for File Format, Color Space, Bit Depth, Resolution and Compression. For now just concentrate on the Color Space option.
If this is set to ProPhoto RGB, it will export how it looks within Lightroom. You will now however, have to go into Photoshops colour settings, and make sure your 'Working Spaces : RGB :' is also set to ProPhoto RGB. This now means that the image in LR and PS is being viewed in the same way. I would recommend at the output section in LR to set the file format to TIFF and bit depth to 8. Unless you're working with a particularly tricky or tonally fine file in which case choose 16bit instead.