Lymphoma (cancer of lymph cells) is a very common cancer in dogs although it usually affects middle aged to older animals. I've listed other possible causes of enlarged nodes below.
Lymphoma is easy to diagnose. A sample of the lymph node is taken by putting a syringe with a needle into the node and drawing a small sample of cells into the syringe. This is smeared on a microscope slide and sent to a laboratory for analysis. Some vets can stain the slide and look at it under a microscope without sending it out. This gets immediate confirmation of lymphoma if that is the problem. This does not require anesthesia or tranquilization and the majority of dogs do not mind the procedure.
The differential diagnosis for swollen lymph nodes includes:
I understand your concern and apologize for not answering this part of your original question. My answer is a bit convoluted. In short, lymphoma (cancer) in dogs does not appear to be contagious; however, there are other causes of swollen lymph nodes that are infectious if not contagious (passing from animal to animal).
Lymphoma is caused by or associated with a viral infection in some species (cats, cattle, chickens, mice, humans), but this has not been shown in dogs. Lymphoma is very common, but the incidence of lymphoma is not increased in dogs who live with affected dogs. There is evidence of a genetic predisposition in some dogs.
Some studies show a relationship between chronic inflammation and lymphoma. For example B cell lymphoma in a dog in one report may have been related to chronic infection with ehrlichia and histoplasma.
Histoplasmosis and Valley fever are fungi that can cause swollen lymph nodes. Infection results from contact with spores in soil. It is not generally considered contagious from animal to animal, but animals in the same household may be exposed to the same source. Richetsial infections (Ehrlichiosis, Rocky Mountain spotted fever), Salmon poisoning, cat scratch disease... etc.
Because lymph node enlargement can be caused by diseases (given in my first response) besides lymphoma, it makes sense to diagnose the cause of the swollen lymph nodes in your dog that is currently affected. An aspirate as described earlier would be a reasonable way to start. Make sure the lab doing the analysis for fungal and bacterial infections. If an aspirate does not provide enough material, a lymph node biopsy or removal with submission for histopathology would provide the needed material.
I'd appreciate hearing the outcome of the biopsy. I don't know if you can add it to this thread or not.
My thoughts are with you and your pups. I know all too well how hard it is to lose pupper friends.