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According to Apple's tech

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According to Apple's tech specs, the iMac Retina 5K won't support the native resolution of this monitor: "Simultaneously supports full native resolution on the built-in display and up to 3840 by 2160 pixels on an external display". Note that the support stated for an external display is UHD, not DCI 4K.

Both DCI 4K and UHD are referred to as 4K but are two different resolution standards. DCI 4K is a professional production and cinema standard, while UHD is a consumer display and broadcast standard. In short, UHD isn't 4K although it is often called UHD 4k. There are also differences besides resolution between the standards: video compression, bitrates, bit depth, chroma subsampling, color space, etc.

LG quotes a native resolution of 4096 x 2160 (DCI 4K): "The 31MU97 delivers 4K (4096 x 2160) resolution...displays over four times the resolution of standard 1920 x1080 FHD, and over half a million more pixels than UHD resolution (3840 x 2160)".

A resolution of 3840 x 2160 works out to an aspect ratio of 16:9. LG quotes an aspect ratio of 17:9. This likely means that the maximum iMac 5K eternal output will be letterboxed (black bars on the sides) on this monitor, unless Apple provides a software scaling solution.

Note the LG 31MU97 4K display uses a Display Port to Mini DisplayPort cable for connection to a computer.

https://www.apple.com/imac-with-retina/specs/
http://www.lg.com/us/monitors/lg-31MU97-B-4k-led-monitor

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