Can I have two 4K and one 5K LG displays on a MacBook Pro 15 2016?
Short answer

Yes, this should be fine.

Long answer

It's not just about whether they're 4K or 5K displays, it's also about the resolution you run them at and possibly if you connect multiple displays on the same physical side since this KB mentions for two 5K displays, they must be connected on opposite sides of the hardware.


https://support.apple.com/en-us/HT207448 - LG UltraFine 5K Display
https://support.apple.com/en-us/HT207447 - LG UltraFine 4K Display


Officially, your model MBP supports up to two displays at 5120x2880 pixels at 60 Hz or up to four displays at 4096x2304 pixels at 60 Hz, one on the left Thunderbolt 3 bus, one on the right Thunderbolt 3 bus.

Your model MBP comes with an integrated Intel HD Graphics 530 GPU and either an AMD Radeon Pro 450, 455, or 460. The integrated Intel HD Graphics 530 GPU will use up to 1.5 GB of your main RAM, while both the Radeon Pro 450 and 455 have 2 GB of dedicated GDDR5 memory and the Radeon Pro 460 has 4 GB of dedicated GDDR5 memory.

At the risk of oversimplifying things, assuming you intend to run the 5K display at 5120x2880 pixels and both 4K displays at 4096x2304 pixels, this equates to a total of 33,619,968 pixels. This is actually less than the 37,748,736 pixels you'd need to power if you were using four 4K displays at 4096x2304. This assumes you intend to use your MBP in clamshell mode, as opposed to also powering the internal display and the external display simultaneously. 

Obviously, if you have the Radeon Pro 460 your MBP will manage this configuration better than it would with one of the other GPUs. However, all GPUs should be fine - it's just that if you have the Radeon Pro 460 there will be less heat produced and therefore your fans won't need to spin as fast. Finally, if you have the Radeon Pro 460 then you'll be able to simultaneously manage more graphics intensive tasks on all displays more smoothly than you would with one of the others.