This website just deleted my response, I am a bit more concise the second time.

Yup, you got a flat mount on the frame and a post mount brake.

If Lynskey wants to charge you for the post mount, you might consider an adapter instead. I am guessing that this will work but since I have no actual experience with this adapter, I am only guessing.
https://www.trpcycling.com/product/f...mount-adapter/