Get Your Dog Care Questions Answered by Experts
The simple answer is no, I would not recommend surgery on a lipoma on the flank. It is not in an area that will interfere with movement and the tumor is not malignant. Removing a large lipoma involves significant surgery and recovery time. The benefits (cosmetic only and the dog doesn't care) do not outweigh the risks (anesthesia, extensive surgery, infection, pain, surgical site breakdown).
Let me know if you have follow up questions.
How much do you think the tumor weights. Large lipomas rarely weigh more than a couple pounds. Fat isn't very dense or heavy. It would have to be extremely large (basketball size or larger) to make the benefit of removal outweigh risks.
It will not increase the risk of arthritis. At 10, he may well have some arthritis.
Reducing 5 (over)weight pounds would be more beneficial than removing the tumor. This can be done by decreasing intake by 10-20% and cutting out snacks.
He should not be short of breath and this is not related to a lipoma on the flank. If he has not been walking half a mile regularly, he may be out of shape and the extra body weight doesn't help. However, I'd be concerned about a heart or respiratory problem assuming it isn't hot and humid where you are. Has the vet listened to his heart and lungs? Does he breathe with effort at rest? Does he wheeze? A chest x'ray might be indicated if respiratory problems are suspected.