Hello, my name is***** and I have over 20 years of experience as a veterinarian. I understand that you are concerned about Lily looking like she is feeding pups and two of her mammary glands being very firm and swollen, even though she isn't pregnant. I think that she is experiencing a false pregnancy.
This can occur after a normal heat cycle, even without a male being anywhere near her.
This is because hormonal changes in a dog are very similar whether they are bred or not.
In a pregnant dog the female's hormones fall off and the pups respond with their own hormones which leads to delivery.
In a nonpregnant dog there just isn't any pup stimulation. But some dog's bodies get confused and they feel like they are pregnant.
They may pick a toy to mother, even build a nest and produce milk.
We do know that if a bitch's mother had false pregnancies then she is likely to have them as well. And once they have one false pregnancy they are likely to have one with every heat cycle where a successful breeding doesn't take place.
It doesn't mean that she isn't fertile or that there are hormonal problems with her. She could be successfully bred on her next heat if you wanted to.
If you aren't going to breed her then I do recommend spaying her to avoid subsequent false pregnancies.
However there really isn't anything that you can do now to change her behavior now. Even spaying her at this point won't change things now as the hormones already produced and circulating in her body are the problem. But spaying her after this false pregnancy will prevent further episodes.
Milk in dogs is produced on demand, meaning that she is probably licking herself because it is uncomfortable, and that is a stimulant will lead to more milk being produced. It is possible that she has developed mastitis, or an infection of the mammary glands in the two glands that are very hard and swollen.
I recommend placing an elizabethan collar (lampshade collar, or cone of shame) in her so she cannot lick her mammary chain any more. Lack of stimulation and back pressure from milk not being expressed should help decrease and eventually lead to stopping milk production.
If she is running a fever, has a foul discharge from her hard firm, mammary glands, and they are painful then they may indeed be infected secondarily. To soothe them tonight and reduce inflammation you can put used tea bags on them or cabbage leaves soaked in cool water. Either of these will help her feel a bit better.
As long as she is still eating and drinking and not running a high fever (greater than 104F rectally) she can wait until morning to see her veterinarian. But if she is very lethargic, has a high fever and is refusing to eat and drink then an emergency visit tonight is indicated.
Please let me know if you have any further questions.