How can I use my MacBook Pro (Retina, 13-inch, Mid 2014) with the LG UltraFine 4K display? Is it possible at all to use the LG UltraFine 4K display with my MacBook Pro (Retina, 13-inch, Mid 2014)?
No, this is not possible with LG's 4K Display since it is usb-c only and not thunderbolt.
Apple officially states that you are able to connect a LG UltraFine 5K Display since the thunderbolt 2 to 3 adapter works to connect them:

3840 x 2160 @ 60Hz
With the Apple Thunderbolt 3 (USB-C) to Thunderbolt
2 Adapter and a Thunderbolt cable, you can use the LG UltraFine 5K
Display at 4K and lower resolutions with these Mac models:
Mac Pro
(Late 2013) macOS 10.12.4 or later is recommended.
MacBook Pro
(Retina, 15-inch, Mid 2014) and later
MacBook Pro (Retina, 13-inch,
Mid 2014) and later
iMac (Retina, 27-inch, Late 2014) and later
iMac
(Retina, 21.5-inch, Late 2015)
iMac (21.5-inch, Late 2015)
MacBook Air
(13-inch, Early 2015)
MacBook Air (11-inch, Early 2015)


The necessary adapters for the 5K Display can be found here:

Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter



Apple Thunderbolt Cable (2.0 m) - White