My dog is vomiting blood. What are the causes and when to see a vet?

Poor guy. Sometimes the vomiting alone can cause a bit of blood in the following vomit due to irritation in the stomach or esophagus. The vomiting wouldn't be related to the lyme disease, and the egg whites are unlikely to be related either (although possible if Nugget has a very weak stomach - dogs generally don't do great with any food changes). I would be concerned about something stuck in his intestines, intestinal parasites, eating other things he shouldn't have, or even metabolic/organ issues. Often with temporary vomiting, we don't find out an underlying cause, but still need to look for problems that could be serious before starting treatment.

I would make sure Nugget has access to lot of water tonight and monitor for continued vomiting, diarrhea, lethargy, and decreased appetite. If he's not back to his normal self tomorrow, he should visit a vet clinic for a check up. They may want to take abdominal x-rays and run some blood work. If he's vomiting non-stop tonight to seems very lethargic, I would recommend going to an emergency clinic.

Let me know if this was helpful and definitely post another question with more information or schedule a consultation if you'd like more help. I hope Nugget is feeling better soon!