How much VRAM does the card have, and what resolution and texture quality are you running at? Most VRAM is taken up by textures, and anisotropic filtering is VRAM-intensive (it creates multiple skewed versions of the texture and stores them in VRAM), requiring more memory than MIP mapping (which is what bi/trilinear filtering uses and nearly doubles the VRAM requirement for a texture).
https://en.wikipedia.org/wiki/Anisotropic_filtering
If your card is running low on VRAM, it will begin dumping textures to make room. You will then experience lag any time it needs to re-load the texture from main memory (or even the disk) and re-generate the anisotropic texture maps.
VRAM can most easily be freed up by lowering texture quality (biggest impact - one notch down in quality requires about 1/4 the VRAM) or reducing anisotropic filter quality. If either of those eliminates the problem, then most likely you were running out of VRAM.
The problem can also happen when the game needs to pull new textures off the disk. Since the amount of time that takes is unpredictable, most games resort to using a loading screen (game is divided into zones which used a fixed number of textures, and when you enter it VRAM is cleared and the new textures read off disk and loaded while the player sits at a loading screen). But for a game like Arkham Knight without loading screens, the textures are dynamically loaded and dumped as the player moves around the game world and approaches and leaves areas where certain textures are needed. If your drive is slow or fragmented, this process might not be happening quickly enough and the game will freeze momentarily while it waits for the dump/load to finish. (Low VRAM will also exacerbate this condition. Since fewer textures can be held in VRAM, it can only hold textures for a smaller region of the game world, meaning they need to be dumped/loaded more frequently as you move around.)
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