Oh my...First of all, take a breath and a step-back for a minute. There are a few things that you need to be certain of before you agree to any surgery or treatments, especially removal of an eyeball...I'm very sorry this is happening to you and your little baby, but if we on this forum have learned anything over and over and over again, it's that when it comes to Veterinarians and birds, if the Vet is not either a Board-Certified Avian Vet or at the very least an Avian Specialist Vet who sees/treats ONLY birds, then you absolutely need to get a second opinion from the closest CAV or Avian Specialist to you...Is this vet either a Certified Avian Vet or an Avian Specialist Vet? Or is this Vet an "Exotics" Vet who sees all types of animals like reptiles, birds, rodents, primates, etc.?
There is a thread in this Conure forum right now where a senior-member's/moderator's Black-Capped Conure suddenly became ill during the holiday, and their regular CAV wasn't available, so they took him to an Animal-Hospital and saw an "Exotics" Vet, who took blood from their bird but took it from the bird's toenail, which is totally the wrong way, and the bird's Uric Acid level came back at a level that was so high that this Exotics Vet told them that he had severe, end-stage Kidney Disease, and they were actually talking about euthanizing him...Luckily our member decided to do nothing until her CAV was available in a day or two, and when they took their bird to their CAV and he drew blood the correct way (from the bird's neck with no sedation/anesthesia necessary at all, takes 30 seconds), the bird's Uric Acid and everything else came back completely normal...Turns out that their bird had a simple infection that is now being treated with antibiotics and their bird is perfectly fine now...But if they had been someone who was less experienced with birds and bird medicine, they very likely would have chosen to euthanize their bird because they wouldn't want him to suffer from Kidney Failure and die a long, painful death...and they would have killed their bird who only had a simple bacterial infection that would have been easily treated...And we see this almost every day on this forum, simply because Avian medicine is so different than any other type of Veterinary medicine, it's very specialized, and it requires a Vet with extra education and training in Avian medicine. Exotics Vets in the US have NO extra education or training in Avian medicine at all. They are simply general vets who "see" all types of animals. That's it.
***So if this Vet is not a CAV or Avian Specialist who sees only birds, but rather an Exotics Vet or General Vet, then you absolutely need to find the closest one to you for a second opinion. That's a no-brainer...Also, has your bird been acting at all sick or unusual in any way?
****Big question: Did this Vet draw blood from your bird and run Blood-Work? What exactly did they do? Without running any Blood-Work they are basing a diagnosis of Lymphoma on simply looking at your bird's eye? Lymphoma is a very specific type of cancer that is easily diagnosed; it's not like having a cancerous growth/mass/tumor and trying to figure out where the source of the cancer originally started, etc. Lymphoma is a specific neoplasia, and in birds it usually effects much older birds, and typically effects their livers, spleens, and kidneys...But the main point here is that running simple, basic Blood-Work (specifically the CBC) in a bird with any type of Lymphoma should show either Leukocytosis or Lymphocytosis, and the bird is also typically very Anemic as well, even if the bird is completely asymptomatic and not showing any issues with their liver, spleen, kidneys, etc.. So I'm hoping that this Vet did take blood to run routine, basic blood-work???? That should always be step #1 when any type of Lymphoma is suspected...
What exactly did this vet do? What tests did he run?