"A lead," is used to describe something which is considered promising. In a criminal context it means information that may possibly lead to a crime being solved. In a business context, it means a contact or information which may lead you to be able to sell something to somebody. "Following up," on something means that you would study the information and try to exploit it.

"A lead" is your suspicion that something might be true, or might be happening, for example you hear about a job opportunity. It is similar to "a clue". Suppose your friend says: -I hear Microsoft is recruiting new people in X-town. Then, that could be a lead for you, if your looking for a job at Microsoft. You then follow up by calling Microsoft and asking bout job opportunities in X-town. Then you are following up on a lead.