You're speaking with Dr. Michael Salkin. Welcome to JustAnswer. I'm currently typing up my reply.
I'm sorry to hear of this with your hen. To answer you directly, yes, respiratory infections can manifest in myriad ways and secondary bacterial infections are common and may result in deaths. Other body systems can be affected; for instance, infectious bronchitis (coronavirus) can affect the reproductive tract. Mature layers infected with infectious bronchitis will lay eggs with misshapen, soft, wrinkled shells for several weeks. I might conjecture that the "lash egg" may represent such an egg.
Lash eggs, however, aren't really eggs. Please see here: http://www.the-chicken-chick.com/2014/12/salpingitis-lash-eggs-in-backyard.html and let me know what you think came out of your hen.