I am so sorry to hear about Lily's diagnosis.
Hyperthyroidism is a fairly common problem, but can be frustrating to treat and takes some time for the levels to subside, especially if they were quite high to begin with. Not eating is an unusual symptom, since most cats are ravenously hungry, yet losing weight. However, some with the complication of high blood pressure and resulting heart issues can go off their food, and this becomes even more critical, as we obviously need energy to survive, as well as to help balance what is being essentially "stolen" by the high metabolic rate.
So it will take time, possibly days to weeks, for the levels of T4 to drop back to where Lily feels good again. These are days that we sometimes don't have. Appetite stimulants, syringe feedings, etc... are all reasonable, but they don't always work and can be stressful. Worse yet is that the medication, Methimazole, can be irritating to the stomach and can cause other side effects. So now we have another issue that is affecting appetite and energy consumption.
Things that can help.
Some of these kitties have acidic, irritated stomachs, so antacids can be helpful with that symptom.
Using a transdermal methimazole (one that is formulated to be absorbed by the hairless skin in the ear rather than requiring oral dosing) can reduce the stress of pilling them and help prevent the sour stomach. Most times this must be special ordered, so vets will almost always start with the pill, but it is an option to consider.
If we just won't eat, and we feel there are no other major health issues found on bloodwork and the ultrasound, then it may be worth a quick procedure to place an esophagostomy feeding tube. This allows no stress syringe feeding through the tube, which exits from a small incision on the neck, and we can feed thicker more substantive foods (more like gruel than broth). It's a frustrating step with a patient who is fragile, but obviously not eating is not going to be a winner. Medicines can also be administered through the tube, so no more wrestling to pill them. These will also all help to prevent the food aversion that may be developing.
Also, during this medical crisis, please feel comfortable to feed anything she'll eat. She needs calories and energy more than a balanced diet, so if she's a tuna or salmon or turkey eater, that is ok, while we're giving blood pressure medicine and methimazole a chance to work.
I hope this provides some information that may help guide you to the next steps. I've seen great response to medical therapy in most cases, but there is a lag between starting meds and seeing that improvement, and a starving cat is not giving you the luxury of time.
Other complications to this whole thing is hypertrophic cardiomyopathy or a heart muscle disease that is often associated with hyperthyroidism and can have the frustrating side effect of, you guessed it, not eating. You're doing the right things medically, now we need to find the lowest stress, highest energy way to support her body until she shows whether she's going to respond well. I think the above options are the best hope.
Please let me know if there is more detail I can provide or if you have other questions that I didn't touch on.
Hoping for the best for Ms. Lily.
---- Dr. Will