unfortunately I don’t know a sure fire way to know who laid the lash egg unless you catch her in the act. As far as treatment, it requires antibiotics but even with treatment it can still be fatal, or at least mess with the reproductive tract. If you can, maybe call your vet and see what they recommend, maybe they have tips to know who might have laid it?
My only personal experience was a hen that never actually laid a lash egg, she just stopped laying any eggs and slowly started to decline-moving slower, less “pep”, stopped flying up to roost at night. Eventually we decided to cull her and when I caught her I realized all her weight was in her abdomen, she had lost most of her muscle mass despite eating and drinking fine(I felt really bad about missing this sign) so I decided to open her up to see if I could locate the problem. Well I found it- it was a softball sized lash egg stuck inside her. Clearly it had been growing for quite some time-much longer than how long I had noticed her starting to act off, so I don’t think antibiotics would have even touched it in her case.
good luck figuring out who’s it was, I hope you can fix your hen!