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I can understand your frustration but, unfortunately, in veterinary medicine we often times see owners make the decision to put their animals down without pursuing diagnostics. They focus on the "worst case scenario" and do not want to put their loved pets through a ton of testing and invasive procedures.
With that being said, if this were my patient, I would strongly recommend an ultrasound guided aspirate of the mass depending upon its location. You are correct that there can be no diagnosis of cancer without testing, it is as simple as that. Other options for a mass in the lungs could be a cyst, granuloma, benign growth, etc.
I am not certain that rushing into surgery without knowing what you are up against is the best option. Diagnostics and figuring out what it going on is the next best step. If your client wants to pursue this but their vet doesn't have the resources, you might consider a referral practice, specialty clinic, or veterinary school. It may even be possible that this mass can be removed and Buddy can live a long and healthy life.
I hope that helps, please let me know if you have further questions!