Pink/lilac eggs can be caused by stress or excess calcium in the layer's diet. Is there anything you are aware of that may be bothering this hen (or all of them), bullying or anything? Also what are you feeding them? Any supplements?
We've recently added 2 turkeys to the mix, but the hens do the bullying there. The turkeys are VERY calm and sleep out in the run instead of inside the coop. We feed layer crumbles and add some oyster shell on occasion. They also have tomatoes, cucumbers, & watermelon for the occasional treats. No supplements. Nothing has really changed. Other than me not being around them much, & I do actually have 1 hen who's "Momma's girl" that I normally sit with her in my lap often. But idk if she's the one laying them or not.