Jeff-
I'm not very familiar with the TIG welding process, but I'm a mediocre MIG welder at best and could certainly make that handle stick and look like it was never broken off. Your friend should have no problems with it.
1) Remove bolts and clean surfaces of rust with grinder or dremel to bare metal at welding location.
2) Weld through existing bolt-holes attaching handle back to lid.
3) Grind down tops of weld with dremel to match existing surface and allow ground down surface to rust like existing metal or clean up entire area and paint with high-temp paint.
As long as your buddy welds through the existing bolt hole and not around the handle "legs", it will look just like the factory weld. It should be easy since the porcelain is already chipped away giving him room to work without messing up anymore porcelain.