Photoshop and Lightroom correct the color from the document colorspace, and convert that to the colorspace of your display - this way you get the most accurate representation regardless of the display, and it'll look the same to everyone (because they correct for different displays).
Applications that are not color managed just copy the values from the document to the display without any conversion - which means that what you see is highly dependent on each display, and everyone will see something different (because they have different displays).
Because Premiere is not color managed, the default display will look different than color managed applications like Photoshop and Lightroom.
If you are using sRGB or Rec.709 for your document profile, then what you see in Photoshop and Lightroom is probably close to what you would see if you put the output from Premiere on a calibrated video display. If you are using other profiles for your documents (Adobe RGB, ProPhoto, etc.) then you probably need to convert to sRGB or Rec.709 so that it will look correct once output from Premiere.