First, I would use PSD, instead of JPEG, as you will get no compression in the image. I would size that PSD to approximately the Frame Size needed, so that PrPro does not have to Scale it. The Scaling algorithms in LR and PS are better, than those in PrPro, and offer more Scaling choices.
Next, your LR space is color managed, while PrPro's is not. This is probably the reason that you are seeing the difference. To do Color Grading in PrPro, one needs to feed the signal, via FW to an A-D device, that feeds the analog signal to a calibrated NTSC (or PAL) monitor. The Program Monitor, besides not being color managed, is but an emulation, a preview.
Hope that this helps,
Changing LR to export a PSD rather than a JPG worked perfectly. Colors in PPro now exactly as I want. Also, thank you for scaling hint. That was going to be my next question!
Thanks again for the help.
Now, I am personally biased against JPEG, but that comes from decades of print advertising work. I only use that format, when a client needs material for their Web site, and then use PNG more often now. Once, browsers had issues with PNG, but most of those are long retired.
Good luck, and thanks for reporting your success,