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Thank you for using Just Answer. My name is Rebecca; I am a veterinarian. Please give me a moment to type my answer.
I am sorry to hear that Tony has lymphoma. You can use children's nose drops in cats, such as Little Noses: 1 drop once to twice daily.
However, what you describe: walking up to the food, acting interested, but then walking away is what cats do when they are sick, or even dying. When I have a cat patient with a disease like cancer or chronic kidney disease that is eventually going to be terminal, owners ask me what to look for to know when their cats are failing, and that the end may be near. I tell them to watch for this exact behavior, not eating but still going to the bowl to look at or smell the food.
At this point, you can try tempting him with more interesting foods, or heating the food in the microwave to enhance the smell. You can also try appetite stimulants such as mirtazapine or cyproheptadine, which you would get by prescription from your veterinarian.
Let me know what other questions you have.
I have not heard back from you; I hope you were able to see my response. How is Tony doing?