If her red blood cells are low due to a problem with the bone marrow that would be an issue that could cause death but there is no particular reason from what you have written to say that this is her problem.
It sounds like the antibiotic drops are reducing her infection based on her being able to eat some and the lymph node going down.
The liquid iron vitamins help give her the building blocks to make more red blood cells. If she was not on that then you might need a supplement but as it is I'd not do that.
If she seems like she is feeling a bit more active then her body may be making the red blood cells she needs.
You can read about anemia here
From your decription I think you are seeing her getting better on the meds she is on.
I suggest you write down specific questions and bring them to your vet when you go back at the end of the antibiotics. I find that always helps me remember what to ask.
If your dog has gums or tongue that look white, blue, gray or yellow tinted where they are normally pink, has a slow color refill if you press on a pink area of gum or tongue, or is becoming lethargic and non responsive to you then you may want to get the dog in to see your vet again sooner rather than waiting to complete the meds.
Hope this helps you!
You are very welcome and thanks for your accept.
The prednisone helps with immune system issues and this might be an immune related anemia which can be triggered by an infection. So the combination of the pred and the antibiotic sounds like it is helping her.
I hoep she continues to approve and thanks for your above accept!