First Chemo treament while recovering from pneumonia?

I'm hoping someone can provide some feedback based on their caregiving experience. I haven't been able to find information about this anywhere, and I don't want to jump to conclusions about my mother's caregivers. So - my 58 year old mother was admitted to the hospital on Jan 24 for pneumonia. She'd probably already had it for a couple of weeks when she was admitted, so her stay lasted 10 days. While she was there, they discovered that she also had lung cancer, but they'd caught it very early and it had not yet spread anywhere. Before they discharged her from the hospital, they gave her the first round of chemo. They said she handled it very well. So she was discharged on Wednesday the 3rd and on Saturday the 5th she went back to the ER for shortness of breath. By Sunday she was dead. The cause of death on the paperwork is "cardiac arrest", and they say that without an autopsy, they can't say for sure. I can't help but wonder if getting chemo while getting over pneumonia could have caused her death. I have so many questions. I live in CA, and I'll be flying back to GA soon to go through her things and talk to the hospital. (She didn't provide any emergency contact info, so we all just found out on Thursday.) Any feedback anyone has on this would really be appreciated. I know this isn't exactly what this forum is intended for, but no other boards made as much sense. Thank you.