In What's The Difference, Piper expands on the 'to lead' bit of his 'mature masculinity' definition, by giving some qualifying statements to avoid misinterpretation of the word. He expands on all of these, but here are the 9 statements he makes. Some of them might be tricky to get the jist of without reaading what he goes on to say about each point, but for what it's worth, here they are-
'1. Mature masculinity expresses itself not in the demand to be served, but in the strength to serve and to sacrifice for the good of woman.
2. Mature masculinity does not assume the authority of Christ over woman, but advocates it.
3. Mature masculinity does not presume superiority, but mobilises the strengths of others.
4. Mature masculinity does not have to initiate every action, but feels the responsibility to provide a general pattern of innitiative.
5. Mature masculinity accepts the burden of the final say in disagreements between husband and wife, but does not presume to use it in every instance.
6. Mature masculinity expresses its leadership in romantic sexual relations by communicating an aura of strong and tender pursuit.
7. Mature masculinity expresses itself in a family by taking the initiative in disciplining the children when both parents are present and a family standard has been broken.
8. Mature masculinity is sensitive to cultural expressions of masculinity and adapts to them (where no sin is involved) in order to communicate to a woman that a man would like to relate not in any aggressive or perverted way, but with maturity and dignity as a man.
9. Mature masculinity recognises that the call to leadership is a call to repentance and humility and risk-taking.'
Well, there you go. I'm guessing you might find some of those quite easy to discount, but I reckon it's at least thinking through each one of these, and the implications they would have.
If you are gluttons for punishment, here are two talks that Piper gave in 2007, that expand on his views on leadership. I actually think they are great talks. The premise is that as a leader, a man is to be 'lion-hearted' and 'lamb-like' at the same time, as Jesus was.
I love this picture of leadership and headship, because it isn't saying 'I'm the boss', it's saying 'I'm taking the innitiative to serve you'. A good illustration that Piper gives, is Jesus washing the disciples feet. That was pure service, yet He innitiated it, and there would not have been doubt in any body's mind at that moment who the leader was there.