Hello, my name is***** and I have over 20 years of experience as a veterinarian. I understand that you are concerned about the amount of sneezing and twitching of her ear that Lily has been doing for the past 24 hours.
A sneeze simply means that something is irritating her nose. It can be dust, pollens, an irritating, strong smell, increased tearing draining into her nose, a viral, bacterial or fungal infection or a foreign body, a tooth root infection or nasal mass irritating the nasal mucosa. Because she is twitching her ear too she may have fluid build up her ear or an itchy ear along with nasal congestion.
If this were a one time thing then dust, pollen, a strong smell, or increased tearing would be most likely. Since this has lingered I would be more inclined to think of an infection (fungal, bacterial or viral), a foreign body (blade of grass, a grass awn), a tooth root infection, or mass/polyp in her nose or inner ear that is blocking drainage through her eustachian tube (opening between the inner ear and back of the throat/nose.
If she has no, or a little clear, nasal discharge, is eating and drinking normally, and her nose conformation is unchanged (no swelling or bumps) then it may be a viral infection, in which case this should pass on its own after a couple weeks.
You could try giving her an amino acid supplement called L-lysine at a dose of 500mg orally twice daily. If this infection is due to Herpes this amino acid interferes with virus replication and will shorten the infection's duration and severity. Good supplements to try are made by the Viralys brand which comes in a powder to add to the food or a tasty gel.
In the meantime using a humidifier in the room she sleeps in most of the time, and/or taking her into the bathroom with you when you run a hot bath or shower to breathe in steam/humid air can help. That will soothe irritated airways and thin the mucous making it easier for her to breathe.
If she continues to sneeze the next step would be sedation, dental radiographs to look for bad tooth roots, a nasal scope and skull radiographs to look for a foreign body or mass. It may be helpful to collect samples for bacterial and fungal cultures as well.
There is also a chronic inflammatory process (Lymphocytic-plasmacytic rhinitis) we see in some older kitties that responds well to steroid therapy. It is not as common as the other things I listed, and we would need to rule out infectious agents before prescribing high doses of steroids because suppressing the immune system of a cat with an infectious disease could be dangerous.
Please let me know if you have any further questions.