The expression of the purple pigment anthocyanin is quite common in new F lyrata leaves. It will go away as the leaf matures, but the spoiled foliage won't. You have some other cultural issues that are limiting enough that the stress is being made manifest in the necrotic spots on leaf margins. Based on nothing but the odds, it's likely to be over-watering and/or a high level of dissolved salts in the soil solution. Let me know if you want to chase that a little farther.

Al

That happened to mine and it was caused by spider mites. You might be able to see them as very small specs on the undersides of leaves. Sometimes you can't see them at all. And, mostly on new growth, there is webbing (very difficult to see). I wiped down the leaves with a wet washcloth and sprayed with neem oil. I had to do it again about a week later.

I don't doubt your plant had mites, but it's probably a coincidence that the symptoms shown in the image above occurred concurrently with the mite infestation. The symptoms shown above are a common physiological issue and go away as the leaf matures.

Al