Which GPU? I don't believe R9 480's exist. The only 3GB R9 cards I'm aware of are 280's and 280X's.
And the RX480's are 4GB minimum.... so I'm not sure what you meant to type there?
Not sure where Apple come into the mix?
Now that you've mentioned the specific monitor, HDMI 2.0 is of no use to you anyway:
http://4k.com/monitor/a-review-of-the-lg-electronics-ips-digital-cinema-31mu97-b-31-0-inch-screen-led-lit-monitor/
HDMI 1.4 only. So 3840×2160 @ 30Hz / 4096×2160 @ 24 Hz is all you can do while using the HDMI (1.4) input on the monitor.
I don't see why you can't simply run either DP or mDP to achieve 60Hz @ 4K? Card has at least the mDP (whichever GPU it is) and the monitor accepts the input. And DP 1.2 can do 4K @ 75Hz.....
Depending on which GPU you have specifically, it may* have DP 1.3 which can do
3840×2160 @ 120 Hz with 24 bit color
5120×2880 @ 60 Hz with 30 bit
or
7680×4320) @ 30 Hz with 24 bit
*If you meant an R9 card, I believe there's only DP1.2
If you meant an RX480 4GB, then there should be DP1.3/1.4