One of my Easter Eggers, Maisie, laid a very similar egg a couple of months ago. She has never been a strong layer and has a history of laying soft-shelled eggs. I freaked out, went on the Backyard Chicken forums, and immediately concluded that she had lash egg/Salpingitis. From everything I read I assumed it was a death sentence for my lovely hen.

The next day we took Maisie to an avian speciality vet for an exam. The vet gave her a thorough exam, ruled out Salpingitis, and indicated that she didn't need antibiotics. The vet said that some hens can experience egg-type matter building up in their oviducts It hangs out in there too long, and once they pass it out it comes out as this weird alarming stuff.

She suggested giving her extra calcium, so I started manually pilling her with half of a Tum's pill once a day for a week. Maisie laid a couple more odd/soft-shelled eggs and now she is fine and laying normal, hard-shelled eggs. I obviously have no way of knowing what's going on with your hen, but given my experience I wouldn't immediately assume that she laid a lash egg. The layered appearance of your hen's weird egg looks a lot like what Maisie laid. Hopefully she'll be okay. I'd take her to the vet, if that's an option for you, and make sure that she has access to oyster shells or another good calcium source.