LOWOLF, The dpi has no relevance to the image resolution of the raw file. LR processes at the maximum of the raw data captured by your camera. By default however when you choose the edit in PS function LR creats a tiff/jpg/psd file accordingly to your choice and sends the image to photoshop at 24' dpi. So when you view the image in PS and go to image>size the dialog will pop up and show the following (my camera an 8mp olympus)
Pixel Dimensions: width 3264 pixels height 2448 pixels
Document size: width 13.6" height 1'.2"
Resolution: 24' Pixels/inch.
Next make sure the resample image box is unchecked so you do not alter the image pixels.
Change the resolution to 3'' pixels/inch and you will see the "document size" change to 1'.88" X 8.16" which give you the size print you will get if you send to print at 3'' dpi.
Then in LR do the following with the same image, use the export function and choose 3'' dpi without changing the Pixel dimentions in the dialog and you will get the following if you open the exported image in PS.
Image size.
Pixel Dimentions: width 3264 height 2448 pixels
Document size: width 1'.88" height 8.16"
Resolution: 3''
Hope this helps.
If you need to have a larger sized print say 14" by 11" at 3'' dpi, then you will have to resample the image in PS.