Which phase of a Lunar landing mission did NASA rate as being the most risky?
Well you had the link up in space where the lunar module had to turn and link up with the lunar lander. Then you had to fire the thrusters enough to put it on a moon trajectory. Then stop firing to put it in a moon orbit (the orbit was planned so that if it wasn’t fired it would bring them back to earth again as a fail safe). Then the actual landing and take-off and re-linking with the lunar module. I would say the most risky parts are the landing and docking, with the landing being slightly higher on the part that you don’t know the exact land layout. This actually occured during the first lunar landing as Armstrong saw the area that was picked for them to land was strewn with boulders so they moved across and landed farther away to reduce the risk of lander damage (they were only built to take the impact of a landing under moon gravity, so were not the toughest beasts around).