No (except read below). The Thunderbolt 3 to Thunderbolt 2 adapter is only for Thunderbolt devices.
The LG 27UK850 is not a Thunderbolt display. It has 3 inputs: HDMI, DisplayPort, and USB-C with DisplayPort alt mode (not Thunderbolt).
The USB-C port of the LG 27UK850 cannot be used to power the MacBook Pro 2015. It can be used to power the MacBook or a MacBook Pro 2016 or later (but only provides 60W where the MacBook Pro might consume more during heavy usage).
For video output to the display, the simplest connection to your MacBook Pro 2015 to the LG 27UK850 can be done with a Mini DisplayPort to DisplayPort cable (not included). To use the USB downstream ports of the display (for keyboard or mouse or thumb drive or whatever you like), you need to connect a USB-C to USB-A cable (not included). The downstream ports will work as USB 3.0 (5Gbps) in this configuration.
There is a way to get video over USB-C to the LG 27UK850 from the MacBook Pro 2015. Connect a Thunderbolt 3 device that has two Thunderbolt 3 ports (such as a Thunderbolt 3 dock or RAID drive) to the MacBook Pro 2015 using the Apple Thunderbolt 3 to Thunderbolt 2 adapter. The second Thunderbolt 3 port of the Thunderbolt 3 device can be used to connect a USB-C cable to the LG 27UK850 for video and USB data.
Note that if you're using USB-C for video, then the downstream USB ports of the LG 27UK850 can only work as USB 2.0 (480 Mbps). This is because a 4K 60Hz display requires all four super-speed lines of the USB-C cable for the DisplayPort signal.