When you 'take the lead' it means you occupy a position that is in advance or head of others.  When you 'take the lead' it can mean you have become the leader and intend to guide others, or that you are in the most advantageous or winning position for example, in a race.  To 'take point on' something is to assume an important or key position, usually one which is the most exposed or vulnerable in a group.  To 'take point on' is an expression usually used in military situations but might be heard in a business context when someone is expressing that they intend to take the lead or become responsible for something.

1. Sharon took the lead in the race near the finish line and held on to secure a great victory.
2. Maria generally takes point on leading any local issues and bringing them up with the council.

1. I want you to take point in these negotiations. I feel that the time is right for you to step up to the plate.
2. Due to their highly skilled workforce and innovative leadership, the company have taken the lead in developing this new technology.