I'm sorry, I didn't mean to make light of your question. My answer seemed to come across that way! The tumor is obviously causing some discomfort (even if it's only slight), and is in an awkward place. Like I said, some lipomas don't increase in size, and if not, it might be liveable-with, rather than opting for surgery? I don't know.
But after getting your vet's advice, then it's a difficult thing....she thinks it may easily grow, and the best option would be to take it off now? Or wait and see if it grows or not.....in which case it may be a more difficult surgery.
I don't know.
Yes, dogs' tails are sensitive, and so is the anal area. But if you do decide to have it removed right now, then the area will be sore for a while, and the vet may give your dog stool-softeners, to make defecation easier post-surgery while the sutured area heals. But unless nerves are damaged during surgery (and I am sure your vet would take good care ) then it would heal probably just fine afterwards.
I have a dog who also has lipomas (or fatty tumors) She has three of these, not terribly big. The largest is about 1" diameter. They have not increased in size in 5-6 years. They haven't needed to be removed. Maybe you could hold fire until that tumor shows any signs of enlarging? It may not.
I don't know of an alternative treatment for lipomas, but I did notice that while a few years ago when my dog developed these three tumors, she was eating pretty low-quality food at the time. I started feeding her very high quality food instead, and she didn't develop any more lipomas. Now that could be just co-incidental, or it could be as a result of low-cholesterol "good" fats now in her diet instead of the dubious ingredients, and possibly "bad" fats in store-bought food? I'm not sure.
I don't know what causes lipomas. Some breeds are more prone to them than others. I don't know if they can develop as a side-effect of any kind of medication or not.