Can't you use the new TB2 to TB3/USB-C adapter cable between your Macbook's TB2 port and the LG's USB-C port? That should let you drive the monitor at 5K.
http://www.apple.com/shop/product/MMEL2AM/A/thunderbolt-3-usb-c-to-thunderbolt-2-adapter
The Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter lets you connect Thunderbolt and Thunderbolt 2 devices — external hard drives and Thunderbolt displays, for example — to any of the Thunderbolt 3 (USB-C) ports on your MacBook Pro. As a bidirectional adapter, it can also connect new Thunderbolt 3 devices to a Mac with a Thunderbolt or Thunderbolt 2 port.*