Is a painless lump on the gum of an 11-year-old boy normal if it has been there 4 weeks and hasn't shrunk even after a course of antibiotics from the dentist who thought it was caused by an abscess?

If it is painless then I seriously doubt that it is an abscess? If the antibiotics have not decreased the size then it could very well be just a bony protrusion that is just now developing and is normal. Another possibility is that it could possibly be the result of a cracked root on that tooth. I suggest that you have a periodontist check this out. An x-ray will show if the root is cracked.