First, I think you mean PPI or pixels per inch, as DPI (or dots per inch) is completely meaningless here
Lightroom does not display PPI of a photo (as far as I know) because you don't need it in Lightroom until you print. Even then, if you have enough pixels, the PPI in the file is irrelevant. The only thing that really matters is the computed PPI. For example, if you want to print 4x6 inches, and the generally accepted standard of quality is 300 PPI, then the photo must have 1200x1800 pixels, or more. So, you can determine the computed PPI simply by dividing the number of pixels by the number of inches.