HI, I'm not nearly as knowledgeable as some of the others that have been helping you, but I know a little. Lash material is usually kind of yellowish semi-solid material that forms when a hen has a reproductive infection like salpingitis. It's kind of like a hard cheesy substance and it's made of solidified pus as I understand it. When a hen passes it, it's called a lash egg although it's not an egg and is usually not shaped much like an egg. It can have a tail-shaped extrusion at one end, I believe that's what
@Wyorp Rock is describing. Antibiotics can help, but she'll have to discuss that with you.
How's your hen doing tonight? Did you get some calcium into her? You can just pop those calcium citrate tablets right into her beak, she can swallow them no problem. Did you know a chicken can swallow a mouse or a frog whole? Yup, those tablets are not even a challenge.