Why doesn't lead appear in my technical tree? 
You complete a mission by launching your core (usually on an multiple of 10 waves). The resources in your core at that time are launched and can be spent on upgrades. Late in the game, like fellow_human said, you can research a launch pad that can actively launch materials into space while you're still playing the mission. Launched materials can be used for upgrades while you're in the middle of a mission.