I'm sorry to hear that your pup Lucy has rubbed some areas on her back of raw. These is probably a hot spot or superficial pyoderma lesion.
Hot spots are caused by the skin getting wet, sometimes from swimming or bathing and not getting dried off properly but most of the time they come from a dog licking, chewing or scratching an itchy area and breaking the skin barrier due to an allergic reaction of some type, allowing bacteria that normally live on the skin to get in the skin and thrive.
If these are hot spots then getting her to stop scratching and allowing the skin to heal will help in resolving them. This likely involves placing an elizabethan (lampshade or cone of shame) collar so she cannot reach them since she is licking the area and treating the underlying allergy.
Allergies are the most common cause of itchy skin. I'll give you an allergy rundown of likely causes for skin troubles. She may have more than one allergy given how symptomatic she is now. Dogs that have one allergy often develop several with time. The effect of multiple allergies aren't additive, they actually compound one another.
Allergies are not something that we cure, we can only control them so they can be quite frustrating.
Even if you don't see fleas I do recommend using protection, especially given the affected area. Fleas tend to congregate around the back of the dog, at the tail head area. They are the most common allergen and it only takes one bite a month to make an allergic dog scratch so I recommend using flea prevention even if you never see one again. Revolution, Frontline Plus, Advantage II or Advantix are excellent topicals, and another option is the new Seresto flea and tick collar that works for 6-8 months continuously. I don't normally recommend collars but this one works very well without toxic side effects for most dogs. Capstar is great for quickly knocking down a large adult population, but unfortunately its effects are short lived. Don't use over the counter products, especially Hartz or Sargents, as most are ineffective if not toxic.
Even when the fleas are gone the allergic reaction can linger for weeks. I'll address how to help with that too.
Other allergens can be inhaled (like grass pollen, dust mites or molds).
You can use a combination of antihistamines and high doses of omega-3 fatty acids to help with the symptoms of flea allergy and inhaled allergies.
In combination fatty acids and antihistamines work synergistically, much better than either one alone. If her symptoms worsen seasonally I would think that inhaled allergens are a part of her problem.
You can try:
1)Benadryl (diphenhydramine only don't use the combination products with decongestants and/or acetaminophen as they can be toxic) at a dose of 1mg to 2mg per pound or one 25mg capsule per 15-25 pounds of body weight orally every 8 hours. Dogs take a much higher dose per pound of body weight compared to people so don't let the size of the dose he would need concern you.
OR 2)Claritin (loratidine) at 5mg per 25 pound dog once or twice daily.
OR 3)Hydroxyzine at 1mg per pound orally every 8 hours.
OR 4) Chlorpheniramine at 4mg to 8mg per dog once or twice daily.
OR 5) Zyrtec (Cetirizine hydrochloride) at 1/2 mg per pound of body weight orally every 24 hours. That would be one 10mg tablet per 20 pounds of body weight. Make sure it is NOT the formulation with a decongestant (such as Zyrtec-D) because dogs cannot tolerate decongestants.
Some dogs do better on one antihistamine rather than another. Give the one you pick a week trial and if it isn't working try another. Be aware antihistamines can cause sleepiness or hyperactivity in some dogs. These side effects do wear off with repeated use.
Omega-3 fatty acids are fish oil products. 3V by DVM or Derm Caps ES are good brand name products. Use the high end of the dosing schedule for your pup's weight, which means if he is between doses go with the higher one. I recommend a dose based upon the EPA portion (eicosapentanoic acid) of the supplement as if we do that the rest of the supplement will be properly balanced. Give her 20mg of EPA per pound of body weight per day. For example an 18 pound dog could take 360mg of EPA per day.
Clip the hair around and over the raw hot spot lesions very short and use a solution mix of Betadine solution (povidine iodine solution) and warm water, made to look like weak tea. Clean the affected areas twice daily. Make sure you get the solution, not the scrub. This is an antibacterial and will dry the lesions out to allow them to heal. No need to rinse this, let it dry on her skin. It does stain horribly though so you probably want to do this outside. Clipping the hair stops bacteria from wicking into the site and allows the skin to breathe and dry.
In cases where the infection gets deeper than the surface of the skin oral antibiotics may be needed to treat deeper infection. If she isn't significantly better in 3-4 days he should see his family veterinarian.
While she may have food allergies most dogs with food allergies tend to have itchy paws, face, neck and perianal area. The lower back is not the usual site for a food allergy. Even though some pet food companies may try to convince you otherwise there are no magic hypoallergenic food ingredients. Grain free diets are NOT hypoallergenic. Many dogs are allergic to a particular protein in a food. A food allergy reaction is based upon the dog's body recognizing an allergen, so they must have been exposed to it before. Prescription foods are hydrolyzed, or broken down so the body cannot recognize the allergen, or they use very unusual ingredients that the dog cannot have been exposed to in the past. They cannot develop an allergy to something they have never been exposed to.
If you believe food allergies may be part of her problem you could try a true hypoallergenic diet like Hills z/d or Purina Veterinary Diets HA. No treats, flavored medication or bones while on the diet and it must be used for a least 12 to 16 weeks to see the full effects. Most clients do report some improvement in 4 to 6 weeks.
Over the counter foods may be labeled hypoallergenic but they are unlikely to truly be so.
The trouble with "limited ingredient", "hypoallergenic" or "low allergy" pet store brands is that the same machinery is used on multiple lots of food without sterilization cleaning in between. So for example even if a food says it has salmon and rice if the previous batch had beef and corn then you will get traces of those ingredients in your bag of food. Not a big deal if your dog isn't allergic to those ingredients but a waste of money thinking that the food was hypoallergenic, and not good for your dog if those happen to be allergens for your dog.
The veterinary brand true hypoallergenic foods are more expensive because it isn't cheap to thoroughly remove all traces of a previous food mixture from the machines used to process food or to hydrolyze the proteins in the food. And the only ingredients in that food, even at a trace level, are what is listed on the bag.
In your pup's case although she had mange previously this is unlikely to be the issue now, as this is not the typical area we see mnge lesions. I highly suspect flea bite allergy given that she hasn't had preventatives applied yet, and this is flea high season.
Please let me know if you have any further questions.