The 3 valve 5.4l is usually NOT a simple R&R.
They only need to be changed every 100,000 miles, so I would price out a Ford dealer or mechanic that has the broken plug removal kit.
If you want to do it yourself then for sure get the broken plug removal kit first, you can take it back if you don't need it.
Ford has a TSB
Loosening plug a bit and then spraying some lube in makes sense.
I think the engine should be luke warm, not hot but warm, you can touch it and it feels warm, not burn you fingers, lol.
If using manual socket wrench keep is centered and slowing apply pressure, once it starts to move it should stay hard to turn all the way out, that means plug is coming out in one piece.
It it gets easy to turn, it broke, remove that piece and open the broken spark plug remover kit.