Traditionally, the flesh golem is Alive… its ALIVE!!. Not so with 5e D&D of course, it is just another automaton but made with soggy RAW parts. Too bad of course (some amazing clips and reels of lore just… left on the cutting room floor as it were) – but RAW is RAW.
For reasons i cannot find in the monster description golems cannot accept most healing spells. It must be under ‘general golem characteristics’ or something. I cannot find it. I also searched Stack Exchange a few times to see if this was already answered a few times. Forgive me if i missed it?
Sometimes there are exceptions to general rules. In this case, the 7th level spell Regenerate seems to be pretty darn powerful. New limbs in just two minutes! That’s the stuff.
Now i get that this should NOT work with golems of any other material (such as stone, iron or clay). If it did RAW, i still would not allow it as a DM. But this would be a great way of rebuilding a fleshy-robot-person-thing when lightning can ‘heal’ but not rebuild.