The lead is the program within the type structure. But that doesn't mean that we are the lead function. The ego-personality is something else. I can choose to use the lead function, I have a tool that I can use, but I am not the tool.
Jung has finer distinctions than we are used to, and socionics is limited to the technical and lacks a lot of the psychology of how real individuals with types function. Yet people here are interested in the psychology. That's why I suggest people read Jung first.