Apple - Do Thunderbolt to Display Port cables exist?

There can be no such thing.

Thunderbolt is an active technology, Display Port is passive.
Adding the required circuitry to one end of such a cable would be pointless - it needs both ends to work.

Edit: Now I read your question again…

You have a Thunderbolt machine & a Display Port monitor…

That's Thunderbolt to Display Port not Display Port to Thunderbolt.

In which case DP to DP would be sufficient; the Thunderbolt circuitry would simply be inactive if you used Thunderbolt to Thunderbolt.
Display Port & mini-DP are the same thing, but different sizes.

Tetsujin's answer is not correct. A display port WILL support resolutions up to 4K with the correct cable. Every high end graphics card have display ports as output. The cable must be certified to support 4K resolution otherwise you will not get 2K resolution support on your LG monitor.

Try this setup: Cable Matters DisplayPort to Mini DisplayPort Male to Female Adapter - 6 Inches with a Thunderbolt cable - length of your choice. The adapter plugs into the LG's display port and the female thunderbolt port is connected to the MBA with a male to male thunderbolt cable. Done.

Here is a link to Amazon store to purchase the adapter (Cost is only $9): http://www.amazon.com/Cable-Matters-DisplayPort-Female-Adapter/dp/B014DV2RGG?ie=UTF8&psc=1&redirect=true&ref_=oh_aui_detailpage_o00_s00