P2415Q, Lenovo X1 Carbon, connection options?

@tnchatmonk  All you need is a USB-C to DisplayPort cable, like this one if you're in the US.  With an X1 Carbon you could alternatively get a full Thunderbolt 3 docking station (like the ThinkPad Thunderbolt 3 Dock Gen 2) and connect your display(s) and any other peripherals through that, in which case you'd have video, USB data for all your other connectivity, and power to charge your system all running through a single cable.  But if that convenience isn't worth the cost of a full dock for you, then a simple cable like the one I linked is all you need.

@tnchatmonk  With a rare exception that I'll address, DisplayPort to HDMI cables/adapters can only be used to connect a DisplayPort source to an HDMI display.  Going HDMI source to DisplayPort input does NOT work, and that has nothing to do with Dell systems or displays specifically.  Lenovo should never have suggested that solution.  The reason it doesn't work is that most (but not all) DisplayPort sources support an optional feature called "Dual Mode DisplayPort", which allows that source port to fall back to native HDMI signaling. In most cases, this capability is what is used to allow DisplayPort to HDMI adapters/cables to work.  (The remaining cases are "active" DP to HDMI adapters/cables that incorporate a converter chip so that the source system continues sending a native DisplayPort signal, and the adapter switches it to HDMI.  These adapters are needed when the source port does NOT support Dual Mode DisplayPort or in certain scenarios where it's not allowed to be used, such as AMD EyeFinity setups.)

But looking the opposite direction, HDMI source ports cannot send a native DisplayPort signal, nor do displays accept a native HDMI signal on their DisplayPort input.  So these adapters/cables cannot be used to achieve that setup.  There are a very small handful of active adapters specifically designed to go in this direction of HDMI source to DP display.  But they are more expensive and complicated than the USB-C to DP cable solution I suggested.  Also, running a 4K 60 Hz display in such a setup would require that your system specifically support HDMI 2.0.  Depending on the generation of X1 Carbon you have, it might be limited to HDMI 1.4, which would only allow 4K 30 Hz (or 1440p 60 Hz).