It depends on the kind of processing.
For 3D games, it's best if the display is connected to the eGPU. If the display is connected to the Mac, then the rendering of the game done by the eGPU needs to be sent to the Mac so the Mac can send it to the display. This drops the performance slightly. Higher resolutions will have a greater performance drop.
Other kinds of processing needs to be sent to the Mac anyway so it can be saved to disk so it shouldn't matter where the display is connected.
To connect two 4K USB-C displays to the Blackmagic eGPU will require some extra hardware. I believe the LG 4K displays don't work with a DisplayPort to USB-C cable unless it also includes USB 2.0 so you can't just use a cable like the Moshi USB-C to DisplayPort Cable (which is supposed to be bi-directional). Anyway, you want the cable to include USB 2.0 for audio, brightness control, USB ports.
I've heard that the "Original Huawei VR 2 Computer Connection Cable DP1.2 + USB2.0 to Type-C Cable" (available on e-Bay) works with the LG UltraFine 4K display. You can combine two of those with a Thunderbolt 3 to Dual DisplayPort adapter.
Another option is a USB-C dock that has a USB-C port that supports DisplayPort alt mode. I believe the HP Thunderbolt Dock G2 has such a USB-C port. One USB-C display should connect to that. The other USB-C display should connect to the Thunderbolt 3 port of the dock.
Another option is a Thunderbolt 3 PCIe expansion box that has two Thunderbolt 3 ports and a DisplayPort output, such as the OWC Mercury Helios 3. Install a SUNIX UPD2018 PCIe card. Connect the DisplayPort output of the Helios 3 to the DisplayPort input of the UPD2018. Now you can connect a USB-C display to the USB-C with DisplayPort alt mode output of the UPD2018, and another USB-C display to the second Thunderbolt 3 port of the Helios 3.
The egpu.io forums have more information about eGPUs and the performance difference between displays connected to the eGPU or to the computer.