Yes this monitor will work on your MBP. However, whether it will run it at its "fullest potential" will depend on your specific model. If your MBP has the Radeon R9 M370X graphics card installed (your question doesn't say) then yes it'll take full advantage of this monitor.
Your MBP supports an HDMI-compatible device, including 4K, while using one Thunderbolt display or can support two Thunderbolt displays not in 4k.
In terms of resolution your MBP supports up to 3840x2160 pixels at 30Hz or 4096x2160 pixels at 24Hz (HDMI).
If your MBP has the Radeon R9 M370X graphics card installed then it'll support up to 5120x2880 at 60Hz via Thunderbolt.
The LG display your looking at has both HDMI and Display Port inputs and provides up to 3840x2160 resolution at 60hz.
So, if you do have the Radeon R9 M370X graphics card installed this will be a good choice of display. If you don't, then it'll work but may not be the best choice depending on your needs.