There are reports of LR not performing well on 8 core CPU like the one you have mentioned. You would be better off going for a 4-core CPU. Also, the AMD FX-8350 is not particularly fast compared to other CPUs today, if you can afford a faster CPU, I would advice getting the faster CPU.
What size (in pixels) is your monitor? If it's a standard HD monitor (1920x1080) then you don't really need to spend money on a top notch GPU (for Lightroom's benefit, but perhaps other programs you use might need the GPU, I don't know)
You didn't state what parts of your current system are slow -- exactly which steps in LR are seeing the slowness? Depending on your answer, the problem might be fixed without major upgrade (or not).
The biggest problem is the time that Lr tooks to export a 300ppi 100% image, it's like 1 minute per image while a friend of mine with an i5 6500 (and also 8 gb of ram) does it in 15 secs, in one moment i tought on buying the same i5 but then i saw the fx 8350 and in my country it's $800 cheaper (i5=$4.000 / fx=$3.200)
i'm using a 1920x1080 screen
As you can see my biggest and only problem is my cpu, that's why i planned updating what i mentioned before, i only update the mobo because otherwise i won't be able to use the new cpu, and i also choose the fx over an i5 because the motherboard for the fx is ddr3 so i can end up having 16gb of high level ddr3 ram vs a 8 gb ddr4 stick
*i said high level ddr3 ram because right now i have a 1600 mhz kingston hyperx and if i buy ddr4 i would end up buying a generic one (bc of the price difference)
As I said before, I would not get an 8 core CPU for Lightroom. Avoid them at all costs.