You've doubled (or more) the workload on the system by attaching the external monitor - so, it's completely normal that the system will slow down when it's active.  

Those applications are a challenge for any system, particularly one like this that doesn't have a lot of reserve in the cooling area.  It will throttle as temperatures inevitably rise, as they will under the stress of driving two displays.  Doing so running this heavy a workload is better done on a desktop system, or if a mobile system is essential, on a big, blocky chassis that has a massive heatsink and plenty of fan ventilation.

The choice of graphics processor is handled by the system software - ironically, diverting to the GeForce GPU will likely increase the level of throttling you see.

As for the refresh rate, it's partly dictated by the system hardware and partly dictated by the type of connection to the monitor -- which cable are you using?

@Antonio86 You forgot a crucial piece of information.  Exactly how are you connecting this display to your XPS 15?  What output port on your XPS 15 are you using, what input on your display are you using, and what sort of cable are you using to connect them?  And do you have any dongles, adapters, or multi-purpose hubs involved?

@Antonio86  Never mind, I'll just tell you what you NEED to do in order to get 4K 60 Hz running rather than waiting to hear what you've already done.  You basically have 2 options:

• A USB-C to DisplayPort cable/adapter connected directly to the system, not through any sort of multi-purpose adapter.  (Technically you could also use a USB-C to HDMI 2.0 cable/adapter connected the same way, although I don't recommend this as much.  USB-C ports output DisplayPort natively, which means USB-C to HDMI adapters/cables need to incorporate active signal converter chips, which can cause problems.  USB-C to DP is simpler, and your Lenovo display has a DP input, so just use that.)
• If you want to use that USB-C/TB3 port for other devices, you'd have to get a Thunderbolt 3 docking station like the WD19TB, which would actually allow you to run dual 4K 60 Hz displays.

If you're using a multi-purpose regular USB-C adapter, then that is why you're stuck at 4K 30 Hz.  The reason is that multi-purpose USB-C adapters configure the USB-C link to carry both video and USB 3.x data.  Running USB 3.x over USB-C requires cutting video bandwidth in half.  That's why you'd be limited to 4K 30 Hz in that setup even though you can run 4K 60 Hz with something like a USB-C to DP cable, since in that case you're not trying to run USB 3.x data simultaneously.  And Thunderbolt 3 can carry dual 4K 60 Hz and USB 3.x simultaneously because it's completely different from regular USB-C.

And the HDMI output on the XPS 15 9560 is only HDMI 1.4, which is only enough for 4K 30 Hz or 1440p 60 Hz.  You'd need HDMI 2.0 for 4K 60 Hz, but that didn't arrive on the XPS 15 until the 9570.

@Antonio86  Ah ok.  Yes zooming in on your NVIDIA Control Panel screenshot I can now see that the diagram does seem to show an HDMI port for the Lenovo display.  In terms of a replacement cable, your system doesn't support DP 1.4, so I wouldn't pay a LOT more for that type of cable compared to a USB-C to DP 1.2 cable.  But if you want to buy it for futureproofing, then a DP 1.4 cable will still certainly work with a DP 1.2 system at DP 1.2 speeds.  Good luck!

Thank you very much for your great answer. I'm actually using an HDMI 2.1 8K cable. 

Do you think that a cable USB-C (Thunderbolt 3) to DP 1.4 is a good choice for my laptop?

Thanks