I am sorry to hear you are worried about Lily. I am a veterinarian and will do my best to help.
Are the scabs tiny? You can feel them more than see them? If so, this could be some type of allergic reaction. Does she scratch at them, or do they bother her?
Since they are around her neck, she could be causing them by scratching at her neck. Cats do this sometimes with an ear infection. The only way to tell if she has an ear infection is to look into her ears with a scope; when you look from the outside just with your eyes, you only see about 1/3 of the ear canal and you can't see the ear drum.
Do any other animals ever come into the house, or is she ever near an open door or window? The most common cause of scabs like you describe is an allergic reaction to flea bites. Even if you do not see any fleas, it can still be that; cats that are allergic to fleas will react to even a single flea bite. Putting something like Advantage on her might help. I once saw a cat that was bald, not a flea to be seen! As soon as the owners started putting Advantage on him, all his hair grew back; flea allergy all along.
You can train a cat to like the carrier, and you should consider doing it in case you ever had an emergency. You get a carrier, tie the door open so it can't close on her, put some food and a towel in it, and leave it in an area of the house that is busy, like a kitchen or bathroom. Just leave it, don't touch or move it. First she will be afraid of it, then she will get curious (especially if there is food in there), and most cats eventually will go in, eat, even take catnaps in it. Leave it there for days or weeks, and she should get over her fear of carriers. Then you can put it away, or better yet leave it there if you can. Then getting her into a carrier for a vet wellness check up, or if she is suddenly ill and needs medical attention, or if you have (heaven forbid) a fire or other emergency, and have to get out safely but in a hurry.
If this were my own cat, I would apply Advantage, and see if that helps. If it does not, I would use an otoscope to look into the ears, use a very fine comb to look for scabs or other lesions all over her body. If I had recently bought a different type of cat food, I would go back to the original food; food allergies can also cause these scabs.
Let me know what else I can help with or answer. Rebecca