I am sorry to hear that your girl is sick, and has had two episodes of not eating, lethargy, and this time also vomiting a bubbly sticky white substance.
It sounds like she is vomiting foam. Vomiting foam simply is a mix of air and stomach/esophageal mucous made when she retches, it is not indicative of any disease process but tells us she is quite nauseous.
Possible causes for her symptoms include dietary sensitivities or allergies, or eating things that she should not have like too many fatty table scraps or garbage, bones etc. metabolic organ failures (kidney or liver disease), Addison's disease (hypoadrenocortisim), pancreatitis, inflammatory bowel disease or even infiltrative cancers are other possible causes.
I understand that extensive blood tests and radiographs were not diagnostic with her last episode.
It's important to know exactly what blood tests were done. Routine bloodwork should have picked up kidney or liver disease but pancreatitis and Addison's disease require special testing and inflammatory bowel disease requires a biopsy to diagnose.
Has she gotten anything different to eat or has she gotten into anything that you know of that may have started all of this?
I would be concerned that she is having a reflare of pancreatitis or she has Addison's disease given her history.
I can give you some suggestions but ideally if she isn't coming along quickly over the next couple of days I would recommend checking further blood tests including a blood test for pancreatitis called can spec PL (canine specific pancreatic lipase) which is highly specific for pancreatitis ad rechecking electrolyte levels.
If her electrolyte levels seem unbalanced (high potassium and low sodium) then testing for Addison's disease with a test called an ACTH response test would be reasonable.
If those things are normal then the next step diagnostically would be an abdominal ultrasound and endoscopy to collect intestinal biopsies.
But for now here are some suggestions.
For now to help with gastrointestinal upset and reflux you can give either:
1) Pepcid ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40 to 80 pounds of body weight every 24 hours
These are acid reducers and should help her feel more comfortable. They are quite safe and can be used for a few days if needed. In some cases dogs remain on them long term if this is a repeated problem.
I would pick up all food for now and water for a couple hours to allow her stomach to settle after the acid reducers. In a couple hours you give her water or low salt clear broths like low salt beef or chicken broth to drink, but make sure it is in small amounts only.
If she seems to feel better tomorrow morning offer a bland diet mix of 1/3 boiled, minced, white, skinless chicken or boiled, lean hamburger, all fats drained off the meat after cooking, and 2/3 boiled, plain, white rice, mashed potatoes or pasta mixed with some low salt chicken or beef broth to make it easy to lap up and swallow as well as increase her fluid intake. If she refuses that you can offer a little meat baby food. If she refuses both then don't push it she likely needs to be seen by your family veterinarian.
Probiotics such as Fortiflora, Proviable, or Benebac can be added to the bland diet mix to help replace appropriate bacteria.
If things go well and she eats and seems more comfortable feed her the bland diet for 2 to 3 days then slowly start to mix back in her regular food, a little more at each meal. It should take about 5 to 7 days to slowly convert her back to her regular diet.
If she continues to be lethargic and vomit, runs a fever (more than 103F rectally), or has a tense painful belly then she is not a candidate for home therapy and must see a veterinarian for an examination, diagnostics, injectable anti-nausea drugs intravenous fluids and supportive care.
If you go back to her original food and stop table food and treats and her lethargy and gastrointestinal issues return then you may wish to consider using a using a low irritant food, like Hills or Royal Canin Sensitive stomach formulas. If those aren't enough then she may need Hills i/d or Purina Veterinary Diets EN, or Royal Canin Gastrointestinal formula.
Please let me know if you have any further questions.