I have a Lenovo P51 laptop with the Quadro M2200 graphics card.
I'm wondering if this hardware supports VR gaming?
If not, would it be possible or sensible to use and external graphics box connected over Thunderbolt?
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Your Lenovo P51 Laptop may be able to run VR if you use an external GPU box (also called eGPU's) because you have a Thunderbolt 3 port, which is what that uses.
If you wanted the Razer Core X, you would need to pair it with a minimum of a GTX 1060. I strongly recommend you getting a GTX 1660Ti over the GTX 1060 because new GTX 1060's are hard to find, and going to be expensive for an older piece of hardware. The GTX 1660TI is the best bang for the buck that would run VR.
If you wanted the Gigabyte's GPU box, I would purchase one with an Nvidia GTX 1080, Nvidia GTX 1070 or an AMD RX 580.
These are the GPUs that will work and I recommend, in order of most to least powerful:
I wouldn't buy anything above an RTX 2060 Super without buying a laptop, where at that point, I'd find a laptop with an RTX 2060 or higher in it because you're going to be saving money at that point (and maybe even some bottlenecking from happening).