This is known as a lip fibroma. It is thought to be either viral or genetic, though no defining answer has been found. It does not seem to be contagious.
They will grow until the impede eating. The only known way to deal with it is surgical removal. This is not as difficult as it sounds, a wet towel, and a small sharp pair of scissors, exacto knife, razor knife or razor blade will remove it. Extremely sharp is the key.
Be careful not to remove too much, another angel or at least a good picture of an angel helps as far as guidance. While it sounds traumatic it really is not, probably worse for the fishkeeper than the fish in most cases.
After removal, keep the angel in a separate tank, with daily 50% water changes & a little melafix. A smaller tank will work well for this, after a week all should be healed.