Lightroom is exporting to the sRGB primaries, as you should have it set for importing then into Premiere. That part is correct, but it's not the only crucial part.
The other part is the display gamma the file is designed for. Premiere will default to a strict internal display gamma of 2.4, following the full Rec.709 standards.
What is the gamma Lightroom and/or your monitor are using? I have no way of knowing what your display and monitoring gamma is set for.however. And if there is an option for Rec.709 in Lightroom, use that.