I give chemo to dogs to treat lymphoma daily.
Many different protocols, but the one with the longest median survival time has been the madison-wisconsin protocol.
I’d say the VAST majority of dogs have little to no side effects of chemo, some that so show nausea are sent home on symptomatic meds (such as an anti diarrhea, anti nausea med for 2 days post chemo). The rare animal will not tolerate chemo well, and the protocol will change. However, unlike people more dogs DONT have side effects than do.
However, lymphoma sucks. And at stage 3a, with mets you likely have been warned that “years” is unlikely. I have known and been attached to dogs that have lived 5+ years with it, and I have known dogs to barely make it to 5 days. Altough a lot depends on staging and remission time, I have also known dogs to have good reponse to their rescue protocols as well. Sounds like you are at a great place where they can help you decide the best course of action for your dog. Its a strange disease, what you expect to happen rarely does… its usually the ones who have “little hope” to pull through the longest 
Chemo is a personal choice, after seeing 100’s of dogs go through it, I can absolutley say I am 100% for giving chemo a try. I find the side effects of chemo and a lower prednisone dose is kinder for the dogs than a higher dose of pred alone (which makes them very thirsty, hungry and pee a lot!)…however, there is nothing wrong with NOT doing it either. However saying that, I had a cat who was on prednisone treatment for his cancer…couldnt get the cat to the vets for injections it was far too stressful for him. The turd kept kicking for 3 years despite his “3 month” death sentence.
As far as “going through chemo” its NOT the same as people. Dogs show up to the clinic once a week, or once every 2 weeks. They have a blood sample pulled, then if WBC’s are ok they get a pill or an IV catheter with quick IV injection (vincristine, vinblastine), or a 30 minute injection (adriamycin, carboplatin). Some also can have IM chemo drugs in their protocol. Voila, done. Nothing more stressful than having a heartworm sample and vaccine done. Chemo doesnt hurt, and its not depressing for them either. Usually the dogs are super happy to come in for their visit and treats! Cats on the otherhand…well…nothing makes a cat happy LOL!
You are aiming to extend a life with chemo, however dogs/cats do not know the difference between an extended life and euthanasia. As long as they are not suffering, neither route is wrong or selfish.
Best of luck with your pup, I hope you get many quality months with him!!!